A three weeks' residence at Delaford, where, in his evening hours at least, he had little to do but to calculate the disproportion between thirty-six and seventeen, brought him to Barton in a temper of mind which needed all the improvement in Marianne's looks, all the kindness of her welcome, and all the encouragement of her mother's language, to make it cheerful. Among such friends, however, and such flattery, he did revive. No rumour of Lucy's marriage had yet reached him:—he knew nothing of what had passed; and the first hours of his visit were consequently spent in hearing and in wondering. Every thing was explained to him by Mrs. Dashwood, and he found fresh reason to rejoice in what he had done for Mr. Ferrars, since eventually it promoted the interest of Elinor.
It would be needless to say, that the gentlemen advanced in the good opinion of each other, as they advanced in each other's acquaintance, for it could not be otherwise. Their resemblance in good principles and good sense, in disposition and manner of thinking, would probably have been sufficient to unite them in friendship, without any other attraction; but their being in love with two sisters, and two sisters fond of each other, made that mutual regard inevitable and immediate, which might otherwise have waited the effect of time and judgment.
The letters from town, which a few days before would have made every nerve in Elinor's body thrill with transport, now arrived to be read with less emotion than mirth. Mrs. Jennings wrote to tell the wonderful tale, to vent her honest indignation against the jilting girl, and pour forth her compassion towards poor Mr. Edward, who, she was sure, had quite doted upon the worthless hussy, and was now, by all accounts, almost broken-hearted, at Oxford.— "I do think," she continued, "nothing was ever carried on so sly; for it was but two days before Lucy called and sat a couple of hours with me. Not a soul suspected anything of the matter, not even Nancy, who, poor soul! came crying to me the day after, in a great fright for fear of Mrs. Ferrars, as well as not knowing how to get to Plymouth; for Lucy it seems borrowed all her money before she went off to be married, on purpose we suppose to make a show with, and poor Nancy had not seven shillings in the world;—so I was very glad to give her five guineas to take her down to Exeter, where she thinks of staying three or four weeks with Mrs. Burgess, in hopes, as I tell her, to fall in with the Doctor again. And I must say that Lucy's crossness not to take them along with them in the chaise is worse than all. Poor Mr. Edward! I cannot get him out of my head, but you must send for him to Barton, and Miss Marianne must try to comfort him."
Mr. Dashwood's strains were more solemn. Mrs. Ferrars was the most unfortunate of women—poor Fanny had suffered agonies of sensibility—and he considered the existence of each, under such a blow, with grateful wonder. Robert's offence was unpardonable, but Lucy's was infinitely worse. Neither of them were ever again to be mentioned to Mrs. Ferrars; and even, if she might hereafter be induced to forgive her son, his wife should never be acknowledged as her daughter, nor be permitted to appear in her presence. The secrecy with which everything had been carried on between them, was rationally treated as enormously heightening the crime, because, had any suspicion of it occurred to the others, proper measures would have been taken to prevent the marriage; and he called on Elinor to join with him in regretting that Lucy's engagement with Edward had not rather been fulfilled, than that she should thus be the means of spreading misery farther in the family.— He thus continued:
"Mrs. Ferrars has never yet mentioned Edward's name, which does not surprise us; but, to our great astonishment, not a line has been received from him on the occasion. Perhaps, however, he is kept silent by his fear of offending, and I shall, therefore, give him a hint, by a line to Oxford, that his sister and I both think a letter of proper submission from him, addressed perhaps to Fanny, and by her shewn to her mother, might not be taken amiss; for we all know the tenderness of Mrs. Ferrars's heart, and that she wishes for nothing so much as to be on good terms with her children."
This paragraph was of some importance to the prospects and conduct of Edward. It determined him to attempt a reconciliation, though not exactly in the manner pointed out by their brother and sister.
"A letter of proper submission!" repeated he; "would they have me beg my mother's pardon for Robert's ingratitude to HER, and breach of honour to ME?—I can make no submission—I am grown neither humble nor penitent by what has passed.—I am grown very happy; but that would not interest.—I know of no submission that IS proper for me to make."
"You may certainly ask to be forgiven," said Elinor, "because you have offended;—and I should think you might NOW venture so far as to profess some concern for having ever formed the engagement which drew on you your mother's anger."
He agreed that he might.
"And when she has forgiven you, perhaps a little humility may be convenient while acknowledging a second engagement, almost as imprudent in HER eyes as the first."
He had nothing to urge against it, but still resisted the idea of a letter of proper submission; and therefore, to make it easier to him, as he declared a much greater willingness to make mean concessions by word of mouth than on paper, it was resolved that, instead of writing to Fanny, he should go to London, and personally intreat her good offices in his favour.— "And if they really DO interest themselves," said Marianne, in her new character of candour, "in bringing about a reconciliation, I shall think that even John and Fanny are not entirely without merit."
After a visit on Colonel Brandon's side of only three or four days, the two gentlemen quitted Barton together.— They were to go immediately to Delaford, that Edward might have some personal knowledge of his future home, and assist his patron and friend in deciding on what improvements were needed to it; and from thence, after staying there a couple of nights, he was to proceed on his journey to town.
After a proper resistance on the part of Mrs. Ferrars, just so violent and so steady as to preserve her from that reproach which she always seemed fearful of incurring, the reproach of being too amiable, Edward was admitted to her presence, and pronounced to be again her son.
Her family had of late been exceedingly fluctuating. For many years of her life she had had two sons; but the crime and annihilation of Edward a few weeks ago, had robbed her of one; the similar annihilation of Robert had left her for a fortnight without any; and now, by the resuscitation of Edward, she had one again.
In spite of his being allowed once more to live, however, he did not feel the continuance of his existence secure, till he had revealed his present engagement; for the publication of that circumstance, he feared, might give a sudden turn to his constitution, and carry him off as rapidly as before. With apprehensive caution therefore it was revealed, and he was listened to with unexpected calmness. Mrs. Ferrars at first reasonably endeavoured to dissuade him from marrying Miss Dashwood, by every argument in her power;—told him, that in Miss Morton he would have a woman of higher rank and larger fortune;—and enforced the assertion, by observing that Miss Morton was the daughter of a nobleman with thirty thousand pounds, while Miss Dashwood was only the daughter of a private gentleman with no more than THREE; but when she found that, though perfectly admitting the truth of her representation, he was by no means inclined to be guided by it, she judged it wisest, from the experience of the past, to submit—and therefore, after such an ungracious delay as she owed to her own dignity, and as served to prevent every suspicion of good-will, she issued her decree of consent to the marriage of Edward and Elinor.
What she would engage to do towards augmenting their income was next to be considered; and here it plainly appeared, that though Edward was now her only son, he was by no means her eldest; for while Robert was inevitably endowed with a thousand pounds a-year, not the smallest objection was made against Edward's taking orders for the sake of two hundred and fifty at the utmost; nor was anything promised either for the present or in future, beyond the ten thousand pounds, which had been given with Fanny.
It was as much, however, as was desired, and more than was expected, by Edward and Elinor; and Mrs. Ferrars herself, by her shuffling excuses, seemed the only person surprised at her not giving more.
With an income quite sufficient to their wants thus secured to them, they had nothing to wait for after Edward was in possession of the living, but the readiness of the house, to which Colonel Brandon, with an eager desire for the accommodation of Elinor, was making considerable improvements; and after waiting some time for their completion, after experiencing, as usual, a thousand disappointments and delays from the unaccountable dilatoriness of the workmen, Elinor, as usual, broke through the first positive resolution of not marrying till every thing was ready, and the ceremony took place in Barton church early in the autumn.
The first month after their marriage was spent with their friend at the Mansion-house; from whence they could superintend the progress of the Parsonage, and direct every thing as they liked on the spot;—could chuse papers, project shrubberies, and invent a sweep. Mrs. Jennings's prophecies, though rather jumbled together, were chiefly fulfilled; for she was able to visit Edward and his wife in their Parsonage by Michaelmas, and she found in Elinor and her husband, as she really believed, one of the happiest couples in the world. They had in fact nothing to wish for, but the marriage of Colonel Brandon and Marianne, and rather better pasturage for their cows.
They were visited on their first settling by almost all their relations and friends. Mrs. Ferrars came to inspect the happiness which she was almost ashamed of having authorised; and even the Dashwoods were at the expense of a journey from Sussex to do them honour.
"I will not say that I am disappointed, my dear sister," said John, as they were walking together one morning before the gates of Delaford House, "THAT would be saying too much, for certainly you have been one of the most fortunate young women in the world, as it is. But, I confess, it would give me great pleasure to call Colonel Brandon brother. His property here, his place, his house, every thing is in such respectable and excellent condition!—and his woods!—I have not seen such timber any where in Dorsetshire, as there is now standing in Delaford Hanger!—And though, perhaps, Marianne may not seem exactly the person to attract him—yet I think it would altogether be advisable for you to have them now frequently staying with you, for as Colonel Brandon seems a great deal at home, nobody can tell what may happen—for, when people are much thrown together, and see little of anybody else—and it will always be in your power to set her off to advantage, and so forth;—in short, you may as well give her a chance—You understand me."—
But though Mrs. Ferrars DID come to see them, and always treated them with the make-believe of decent affection, they were never insulted by her real favour and preference. THAT was due to the folly of Robert, and the cunning of his wife; and it was earned by them before many months had passed away. The selfish sagacity of the latter, which had at first drawn Robert into the scrape, was the principal instrument of his deliverance from it; for her respectful humility, assiduous attentions, and endless flatteries, as soon as the smallest opening was given for their exercise, reconciled Mrs. Ferrars to his choice, and re-established him completely in her favour.
The whole of Lucy's behaviour in the affair, and the prosperity which crowned it, therefore, may be held forth as a most encouraging instance of what an earnest, an unceasing attention to self-interest, however its progress may be apparently obstructed, will do in securing every advantage of fortune, with no other sacrifice than that of time and conscience. When Robert first sought her acquaintance, and privately visited her in Bartlett's Buildings, it was only with the view imputed to him by his brother. He merely meant to persuade her to give up the engagement; and as there could be nothing to overcome but the affection of both, he naturally expected that one or two interviews would settle the matter. In that point, however, and that only, he erred;—for though Lucy soon gave him hopes that his eloquence would convince her in TIME, another visit, another conversation, was always wanted to produce this conviction. Some doubts always lingered in her mind when they parted, which could only be removed by another half hour's discourse with himself. His attendance was by this means secured, and the rest followed in course. Instead of talking of Edward, they came gradually to talk only of Robert,—a subject on which he had always more to say than on any other, and in which she soon betrayed an interest even equal to his own; and in short, it became speedily evident to both, that he had entirely supplanted his brother. He was proud of his conquest, proud of tricking Edward, and very proud of marrying privately without his mother's consent. What immediately followed is known. They passed some months in great happiness at Dawlish; for she had many relations and old acquaintances to cut—and he drew several plans for magnificent cottages;—and from thence returning to town, procured the forgiveness of Mrs. Ferrars, by the simple expedient of asking it, which, at Lucy's instigation, was adopted. The forgiveness, at first, indeed, as was reasonable, comprehended only Robert; and Lucy, who had owed his mother no duty and therefore could have transgressed none, still remained some weeks longer unpardoned. But perseverance in humility of conduct and messages, in self-condemnation for Robert's offence, and gratitude for the unkindness she was treated with, procured her in time the haughty notice which overcame her by its graciousness, and led soon afterwards, by rapid degrees, to the highest state of affection and influence. Lucy became as necessary to Mrs. Ferrars, as either Robert or Fanny; and while Edward was never cordially forgiven for having once intended to marry her, and Elinor, though superior to her in fortune and birth, was spoken of as an intruder, SHE was in every thing considered, and always openly acknowledged, to be a favourite child. They settled in town, received very liberal assistance from Mrs. Ferrars, were on the best terms imaginable with the Dashwoods; and setting aside the jealousies and ill-will continually subsisting between Fanny and Lucy, in which their husbands of course took a part, as well as the frequent domestic disagreements between Robert and Lucy themselves, nothing could exceed the harmony in which they all lived together.
What Edward had done to forfeit the right of eldest son, might have puzzled many people to find out; and what Robert had done to succeed to it, might have puzzled them still more. It was an arrangement, however, justified in its effects, if not in its cause; for nothing ever appeared in Robert's style of living or of talking to give a suspicion of his regretting the extent of his income, as either leaving his brother too little, or bringing himself too much;—and if Edward might be judged from the ready discharge of his duties in every particular, from an increasing attachment to his wife and his home, and from the regular cheerfulness of his spirits, he might be supposed no less contented with his lot, no less free from every wish of an exchange.
Elinor's marriage divided her as little from her family as could well be contrived, without rendering the cottage at Barton entirely useless, for her mother and sisters spent much more than half their time with her. Mrs. Dashwood was acting on motives of policy as well as pleasure in the frequency of her visits at Delaford; for her wish of bringing Marianne and Colonel Brandon together was hardly less earnest, though rather more liberal than what John had expressed. It was now her darling object. Precious as was the company of her daughter to her, she desired nothing so much as to give up its constant enjoyment to her valued friend; and to see Marianne settled at the mansion-house was equally the wish of Edward and Elinor. They each felt his sorrows, and their own obligations, and Marianne, by general consent, was to be the reward of all.
With such a confederacy against her—with a knowledge so intimate of his goodness—with a conviction of his fond attachment to herself, which at last, though long after it was observable to everybody else—burst on her—what could she do?
Marianne Dashwood was born to an extraordinary fate. She was born to discover the falsehood of her own opinions, and to counteract, by her conduct, her most favourite maxims. She was born to overcome an affection formed so late in life as at seventeen, and with no sentiment superior to strong esteem and lively friendship, voluntarily to give her hand to another!—and THAT other, a man who had suffered no less than herself under the event of a former attachment, whom, two years before, she had considered too old to be married,—and who still sought the constitutional safeguard of a flannel waistcoat!
But so it was. Instead of falling a sacrifice to an irresistible passion, as once she had fondly flattered herself with expecting,—instead of remaining even for ever with her mother, and finding her only pleasures in retirement and study, as afterwards in her more calm and sober judgment she had determined on,—she found herself at nineteen, submitting to new attachments, entering on new duties, placed in a new home, a wife, the mistress of a family, and the patroness of a village.
Colonel Brandon was now as happy, as all those who best loved him, believed he deserved to be;—in Marianne he was consoled for every past affliction;—her regard and her society restored his mind to animation, and his spirits to cheerfulness; and that Marianne found her own happiness in forming his, was equally the persuasion and delight of each observing friend. Marianne could never love by halves; and her whole heart became, in time, as much devoted to her husband, as it had once been to Willoughby.
Willoughby could not hear of her marriage without a pang; and his punishment was soon afterwards complete in the voluntary forgiveness of Mrs. Smith, who, by stating his marriage with a woman of character, as the source of her clemency, gave him reason for believing that had he behaved with honour towards Marianne, he might at once have been happy and rich. That his repentance of misconduct, which thus brought its own punishment, was sincere, need not be doubted;—nor that he long thought of Colonel Brandon with envy, and of Marianne with regret. But that he was for ever inconsolable, that he fled from society, or contracted an habitual gloom of temper, or died of a broken heart, must not be depended on—for he did neither. He lived to exert, and frequently to enjoy himself. His wife was not always out of humour, nor his home always uncomfortable; and in his breed of horses and dogs, and in sporting of every kind, he found no inconsiderable degree of domestic felicity.
For Marianne, however—in spite of his incivility in surviving her loss—he always retained that decided regard which interested him in every thing that befell her, and made her his secret standard of perfection in woman;—and many a rising beauty would be slighted by him in after-days as bearing no comparison with Mrs. Brandon.
Mrs. Dashwood was prudent enough to remain at the cottage, without attempting a removal to Delaford; and fortunately for Sir John and Mrs. Jennings, when Marianne was taken from them, Margaret had reached an age highly suitable for dancing, and not very ineligible for being supposed to have a lover.
Between Barton and Delaford, there was that constant communication which strong family affection would naturally dictate;—and among the merits and the happiness of Elinor and Marianne, let it not be ranked as the least considerable, that though sisters, and living almost within sight of each other, they could live without disagreement between themselves, or producing coolness between their husbands.
THE END
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JS
- var array = [1,"hello", true];
- array.push("3") #=> 1,"hello", true, "3"
- array.slice(1,3) #=> "hello", true, "3"
- array[0] #=> [1]
- array.indexOf("hello") #=> 1
RUBY
- array = [1,"hello", true]
- array.push("3") #=> 1,"hello", true, "3"
- array.slice(1,3) #=> "hello", true, "3"
- array[0] #=> [1]
- array.index("hello") #=> 1
When defining arrays in Javascript you should remember to use "var" when assinging an array to the vairable, as for ruby you do not need to use the word "var".
JS
- function each(array){
for(i = 0; i < array.length; i++){
console.log(array[i]);
}
}
each(); //calling the function each
- // function declaration. Loads before any of the code gets read.
- #=> 1,"hello", true, "3"
- // another way to do it for better readability
- var each = function(array){
for(i = 0; i < array.length; i++){
console.log(array[i]);
}
}
- // function expression. Loads function when it reaches that line of the function.
RUBY
- array.each {|x| puts x} #=> 1,"hello", true, "3"
With ruby it is easy to use the built in array#each method to iterate over each index of the array. In Javascript we created a function called "each" to loop over the indexs of the array and out put it
explanation
explanation


Visual Fixture Test
This micro-library that gives opportunity to visually test fixtures in your project that have been used for unit-testing your components.
Setup
Installation
To install it execute the following command in Terminal for your project directory, if this library is not included into your package.json
yet
npm install --save-dev confirmitasa/r-visual-fixture-test
Test page
Grab this code to create your test page. Make sure you provide a correct path to the visual-fixture-test.js
and HTMLImports.js
(installed with this bundle) in your file:
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<title>Visual test</title>
<!-- Make sure the filepath is correct -->
<script src="../../node_modules/webcomponents.js/src/HTMLImports/HTMLImports.js"></script>
<!-- This script loads your module code that you want to visually test on your fixtures-->
<script src="../../dist/r-sort-table.bundle.js"></script>
<!-- Make sure the filepath is correct -->
<script src="../../node_modules/r-visual-fixture-test/src/visual-fixture-test.js"></script>
<script>
// use the visual-fixture-test's `testFixture` to create your module's execution context for a fixture
testFixture('table-nested-headers',function(){
var tableTest = new Reportal.SortTable({
source: document.querySelector('table'),
data: [['foo','bar']]
});
});
</script>
<!-- Import necessary fixtures, they'll be automatically added to a dropdown on that page for selection. The first fixture in this import list will load on pageload. Make sure the path is correct-->
<link rel="import" href="../__tests__/fixtures/table-nested-headers.html">
</head>
<!-- Body tag can be left empty, there's nothing you'd need to load here -->
<body></body>
</html>
testFixture()
testFixture()
is a function that lets you load contexts for your module execution on a per-fixture or a global basis. This is the only function you need to use to setup the process.
Named (fixture-specific) context
testFixture('fixture-name', function(){ /* fixture modification is here */ })
: You may pass up to two attributes to the function:
name
- A dash(-
)-concatenated name of the fixture that corresponds to the fixture filename without.html
extension. If fixture is along path../__tests__/fixtures/my-awesome-fixture.html
, the name would bemy-awesome-fixture
. Providing a name makes the fixture execution code be fixture-specific. Pass this argument only if you need a fixture-specific execution configuration. If this option is omitted, it's assumed that the callback function is to be executed for all fixtures imported into the document.callback
- a callback function that will be executed every time the fixture is loaded
// functions will be executed per named fixture
testFixture('my-awesome-fixture', function(){
//code executed only for `my-awesome-fixture.html`
});
testFixture('my-super-awesome-fixture', function(){
//code executed only for `my-super-awesome-fixture.html`
});
Nameless (global) context
testFixture(function(){ ... })
- if you pass only a function callback that does something to the fixture, without providing a name, it will be a default callback for all fixtures (except for those that have named callbacks)
// will executed on all fixtures in the document every time the fixture is loaded.
// It's assumed this callback will be executed for all fixtures that don't have a fixture-specific code.
// There can be only one default (nameless) fixture callback on a page
testFixture(function(){
// fixture processing code
});
Browser Support
This lobrary is intended to work in the latest versions of evergreen browsers. See below for our complete browser support matrix:
| Polyfill | IE10 | IE11+ | Chrome* | Firefox* | Safari 7+* | Chrome Android* | Mobile Safari* |
|---|---|---|---|---|---|---|---|
| HTML Imports | ~ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
*Indicates the current version of the browser
~Indicates support may be flaky.
Commands (configured in package.json)
npm install
installs all dependencies of the projectnpm run docs
generates documentation for your project.js
files that use JSDoc3 comments and puls them intodocs
foldernpm run docs-commit
publishes documentation tohttp://ConfirmitASA.github.io/[RepoName]/
where[RepoName]
is name of your repository as well as name specified inpackage.json -> name
AND[version]
is the version in yourpackage.json
. Please make sure you have thenpm run docs-commit
command configured properly with the correct name of repo to be used there.


IGTracker - UX Case Study
Instagram tracking application
Inspiration
Lots of teens using SNS applications nowadays. They love to use SNS applications like Twitter, Facebook and Instagram. And they really care about their account’s popularity and interest about their account from others. Most of the teens that using SNS believe about ripple effects from their SNS account, and they spend a lot of time to attract more followers on their account.
Design Process
I followed IDEO’s Human-Centered Design process to make my design backed up by feedback, researches and user testing.
#1. Observation
Goal & Audience
IGTracker’s goal is very straightforward and simple — To analyze and track user’s Instagram account’s statistics like Followers, Following, Likes, Comments, etc. Our main target are teens, mostly from USA and aged between 13~25. Also main audience of Instagram, Snapchat and Facebook. Above all, Instagram is the most popular and active application between those targets. We aim our targets by providing an application, which can deeply analyzing their Instagram account’s statistics.
“Try to understand people through observing them. For example, if you’re designing a vacuum cleaner, watch people vacuum.”
Results of surveys by LendEDU
Question 1: Do you make an intentional effort to like people’s Instagram posts who like yours?
Question 2: Do you know someone who deletes Facebook or Instagram posts if they don’t get enough likes?
According to the survey by LendEDU above, it seems most of young people really cares about their Instagram account's popularity. We can find out that those Instagram users check the popularity of posts they posted. They are accustomed to do such 'work'. However, what if they can check and review their accounts overall history of statistics on a single screen, instead of checking their posts one by one?
Persona
I created a potential user of IGTracker based on our main target that I write on above paragraph. Image below is a persona of the potential IGTracker’s user.
Job Stories
I used Jobs to be done framework to understand better our mission as a sight of actual users of our application, IGTracker.
- When I managing my Instagram account, I want to take care about my feeds and followers, So I can keep my followers following on me.
- When I upload a new post on my Instagram, I want to get lots of Likes on it, So I can make my account more popular.
- When someone unfollow my Instagram account without any single word, I want to track those people who unfollowed me, So I can unfollow them either or try harder to keep my followers following me.
#2. Ideation
Main purpose
IGTracker’s main purpose is to provide insights of user’s Instagram account. IGTracker analyze the account’s status like it’s Followers, Blocked users, Comments and likes. And show those information with graph and chart with clean and intuitive user interface.
Brainstorming
Our team began to brainstorming the ideas, based on observations and experiences on prior step. We focused on our target’s needs and desires. There are some points on our main targets(Teens based in USA, aged between 13~25):
- They are used to making social networks with mobile applications like Snapchat, Instagram, Musical.ly and Houseparty.
- They love interactions and gestures like Swiping, Pinching, Expanding, Animations and those are completely natural to them.
- They are expert on those operation system, applications and interactions, but still don’t want to be difficult by complex and hard UX.
Quick UI Concepts
IGTracker is going to release only for iOS platform. Based on iOS Human Interface Guidelines, our team started to make some guidelines for IGTracker application:
- White/negative space clean design, with bold fonts and emoji(Inspired by Snapchat).
- Organized, spaced and easy to read with contrast colors, with the minimalist approach for readable data and graph at a glance.
- Focus on young designs and not only functional design due to our main targets have standards from other applications like Instagram, Snapchat or Facebook.
#3. Rapid Prototyping
Lo-Fi Prototypes
For a quick user testing, our team created some rough prototypes. With InVision application, made them clickable, and started to test it with some testers who love to use Instagram, and care about their popularity. To make sure that our solution is on our target, we focused not to make a detailed and perfect solution and prototypes. (Click image to enlarge )
_a. Dashboard
After the user logs in, this screen is the first screen that user see. In this screen, we summarize the main information that the user needs by graphs:
- Followers Growth
- Unfollowed Me
- Not Following Me Back
- Blocked Me
- Deleted Comments/Likes
It’s not a scrollable screen. We are showing fixed number of mandatory items, to give the user the feel of control on what’s happening with user’s account analytics, on a high level.
For the very first time, we had more graphs on the main screen for more insight than the current design. However, after thinking carefully about what really users need, we decided to offer only 5 graphs in total: 'Followers Growth', 'Unfollowed Me', 'Not Following Me Back', 'Blocked Me' and 'Deleted Comments/Likes'.
1. Followers Growth
The number of followers that are heavily exposed at the top of their Instagram profile is the indicator for them that indicates their popularity on the Instagram. They are very interested in the number of their followers and are sensitive to changes of the numbers. In the 'Followers Growth' graph, you can see at a glance statistics about the overall followers change of the Instagram account.
2. Unfollowed Me
It's an interesting phenomenon, but people really want to know about other people who no longer follow their Instagram account. They feel that their Instagram account is popular when there are many people who follow their account than they follow, and feel satisfied about that. Therefore, they want to find unfollowed users and unfollow them equally. The 'Unfollowed Me' graph provides insight into those statistics.
3. Not Following Me Back
This is similar to let the 'Unfollowed Me' graph on the main screen. When they follow someone, they want him/her to follows them back. The number of followers is very important to them. If someone does not follow me back, they will want to know who it is.
4.  Instagram does not tell users who blocked them. Everyone on Instagram wants to know how many people have blocked them, and who has blocked them.
5. Deleted Comments/Likes
As you can see from the statistics above, the popularity of your post is very important to them. They want to delete posts that do not get satisfactory 'Likes' and 'Comments'. The 'Deleted Comments/Likes' graph shows at a glance the number of posts that have not received satisfactory 'Likes' and 'Comments' and number of deleted Comments / Likes.
_b. Audience/Posts Screen
This screen will have a list of ‘insights’ and ‘analytics’ about the ‘Tab’ that the user just tapped (either ‘Posts’ or ‘Audience’) that the user can access. It’s basically a scroll view that shows the available data options we provide. User can switch to this screen using the Tab Bar, clicking ‘Posts’ or ‘Audience’ tab (both are same screen, only with different data). When pressing one of the actions(tab), it’ll take him to the next screen (c.) in our list.
_c. Inner Analytics Screen
This screen will display the information that user just tapped on prior screen (b.). It’s basically a scroll view that shows a list of the requested information by the user. On this screen, each user profile list contains:
- Name of the user
- If the user follows me or not
- The amount of the likes & comments user gave me
#4. User Feedback
Usability Testing
With the prototypes we created on prior step (#3.), our team had some usability tests with numerous testers. There’s only one condition for testers — love Instagram and spend a lot of time to manage their account on Instagram. This step is critical for us to get more ideas, feedback and information and to better understand the target’s needs.
“If you want to improve a piece of software, all you have to do is watch people using it and see when they grimace, and then you can fix that.” — David Kelley
Feedback
We got some feedback from users during the usability testing. Here’re the lists that we summarized from main feedback.
- Need ‘Switch Account’ button on Dashboard Screen for users who have more than just one account.
- Screens are pretty ‘businesslike’ and boring; in spite of the main targets are teenagers.
- ‘Follow’/’Unfollow’ button is needed on ‘Inner Analytics Screen’ to make user able to follow or unfollow other users immediately.
Improvements
Based on tester’s feedback and opinions, some features are re-designed with Hi-Fi prototypes. (Click image to enlarge )
_a. Dashboard
We added ‘Switch Account’ button on top of the screen for users to switch their accounts if they have more than 1 account. It’s similar with Instagram application — just click and tab another account to switch — so the users can use this feature easily. If the user wants to add a new account, simply tab the last list of the menu ‘Add Account’.
_b. Audience/Posts Screen
No big change has happened. Just organized each tabs (lists), added some details like arrow and font variation.
_c. Inner Analytics Screen
‘Follow’ and ‘Unfollow’ buttons were added on the right side of each user’s list to make user follow or unfollow the other users on this screen, without exit the IGTracker application. We also added more details like numbers of follow and followers of users in the list.
By providing ‘Follow’ and ‘Unfollow’ buttons, users don’t need to switch from IGTracker to Instagram, if they want to follow or unfollow the user on the list. In addition, users can check that the other user follows me or not.
Thumb zone
On the main screen(with the graphs), it's important to keep users can control and watch every analytics and graphs easy and comfortable. Every main activities and information that users need and want to know are on the main screen. I referenced an article of Samantha about 'thumb zone' for this framework.
#5. Iteration
Based on Feedback
With Hi-Fi prototypes, we built another clickable prototype for next usability testing. From now on, keep testing and reflecting user’s feedback is really important for us before our application gets ready to be used.
#6. Implementation
Work In Progress
Although we’re still work in progress, validated data from each steps are implementing right after tests. We’re continuing to observe our testers to validate our application’s usability. Clickable mock-up below is the latest application’s prototype. We’re always opened for many user’s feedback and opinions. I used ProtoPie to create animated GIF image below.
Play with Prototype
Clickable prototype is also available on MarvelApp
What I've learnt
The targets of IGTracker are 'Teens' and 'College students'. We interviewed them (including our friends), observed them, looked at surveys about their use of Instagram, and spent a lot of time thinking about what they really needed in managing their Instagram account. Through observing the actual users and empathizing with them, we felt the importance of insight that they could gain. In addition, found the insight can make the product useful and good to use.
Takeaways
IGTracker is an application for teens in USA who love using SNS applications and spend time with them. Our application will help them to easily get insight about their account’s statistics and interests with clean and detailed user interface.
Thanks for reading my article. If you want to contact me, visit my LinkedIn or just send me an Email to<EMAIL_ADDRESS>For more UX/UI design that I’ve worked, visit my Behance. Hope you enjoyed my article!
Watch Full Design on Behance (2018 ADAA - Semifinalist)
Instagram tracker - UX case study
Selected as an ADAA 2018 Semifinalist
Click Here to Watch on Medium
Clickable prototype is available on MarvelApp
Title : IGTracker - UX case study
Date : August 20, 2017 (2 Weeks)
Tools : Adobe XD, Adobe Photoshop, Adobe Illustrator, Kakao Oven, Studio XID ProtoPie, MarvelApp
Designer : Hyouk Seo (Spemer)
Developer : Roi Mulia


Patient Profile
Personal Information
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Last Name: {{profile.0.LastName }}
Phone: {{profile.0.Phone}}
Address: {{profile.0.Address}}
Medcial Information
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Treatment: {{pro.Ailment }}
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| Overview | Namespace | Class | Index | Help |
| PROTECTED MEMBERS: | CLASSES | STRUCTS | UNIONS | ENUMS | TYPEDEFS | METHODS | STATIC METHODS | DATA | STATIC DATA |
| PRIVATE MEMBERS: | CLASSES | STRUCTS | UNIONS | ENUMS | TYPEDEFS | METHODS | STATIC METHODS | DATA | STATIC DATA |
template< typename T >
com::sun::star::beans::XPropertySet (public) | | com::sun::star::beans::XFastPropertySet (public) | | | | com::sun::star::beans::XPropertyAccess (public) | | | +----+----+--PropertySetMixinImpl (public) | +--PropertySetMixin
| virtual | abstract | interface | template |
| NO | NO | NO | YES |
T
(which must correspond to a UNO interface type).
Methods |
|
| PropertySetMixin( const com::sun::star::uno::Reference< com::sun::star::uno::XComponentContext > & context, Implements implements, const com::sun::star::uno::Sequence< rtl::OUString > & absentOptional ); |
The constructor. |
| ~PropertySetMixin( ); |
The destructor. |
Methods |
|
| PropertySetMixin( PropertySetMixin & ); |
|
| void operator=( PropertySetMixin ); |
Copyright © 2012, The Apache Software Foundation, Licensed under the Apache License, Version 2.0. Apache, the Apache feather logo, Apache OpenOffice and OpenOffice.org are trademarks of The Apache Software Foundation. Other names may be trademarks of their respective owners.


FoosBall
PLAY
(Use left and right arrow keys to play)
Written in vanilla Javascript using HTML5 canvas
By Prashant Baid
Source Code
FoosBall
PLAY AGAIN
Time Left
02:00
Juventus
0
Liverpool
0
Created By
@prashantbaid


The PNG specification defines 18 chunk types. This document is intended to help users who are interested in a particular PNG chunk type. If you have a particular PNG chunk type in mind, you can look here to see what support PyPNG provides for it.
Generated automatically by PyPNG. The IHDR chunk specifies image size, colour model, bit depth, and interlacing. All possible (valid) combinations can be produced with suitable arguments to the png.Writer() class.
Correctly handled when a PNG image is read. Can be generated for a colour type 3 image by using the palette argument to the png.Writer() class. PNG images with colour types other than 3 can also have a PLTE chunk (a suggested palette); it is not currently possible to add a PLTE chunk for these images using PyPNG.
Generated automatically from the pixel data presented to PyPNG. Multiple IDAT chunks (of bounded size) can be generated by using chunk_limit argument to the png.Writer() class.
Generated automatically.
Generated for most colour types when the transparent argument is supplied to the png.Writer() to specify a transparent colour. For colour type 3, colour mapped images, a tRNS chunk will be generated automatically from the palette argument when a palette with alpha (opacity) values is supplied.
Ignored when reading. Not generated.
When reading a PNG image the gAMA chunk is converted to a floating point gamma value; this value is returned in the info dictionary: info['gamma']. When writing, the gamma argument to the png.Writer() class will generate a gAMA chunk.
Ignored when reading. Not generated.
When reading a PNG image the sBIT chunk will make PyPNG rescale the pixel values so that they all have the width implied by the sBIT chunk. It is possible for a PNG image to have an sBIT chunk that specifies 3 different values for the significant bits in each of the 3 colour channels. In this case PyPNG only uses the largest value. When writing a PNG image, an sBIT chunk will be generated if need according to the bitdepth argument specified. Values other than 1, 2, 4, 8, or 16 will generate an sBIT chunk, as will values less than 8 for images with more than one plane.
Ignored when reading. Not generated.
Ignored when reading. Not generated.
Ignored when reading. Not generated.
Ignored when reading. Not generated.
When a PNG image is read, a bKGD chunk will add the background key to the info dictionary. When writing a PNG image, a bKGD chunk will be generated when the background argument is used.
Ignored when reading. Not generated.
Ignored when reading. Not generated.
Ignored when reading. Not generated.
Ignored when reading. Not generated.
Generally it is not possible to generate PNG images with any other chunk types. When reading a PNG image, processing it using the chunk interface, png.Reader.chunks, will allow any chunk to be processed (by user code).


W
aka
L
ending
I
nvestor
ID:
1
Zillah Poliquit
Daily Collectables
Remaining Balance
500
8000
Summary
Date
Collector Assigned
Daily Payment
Remaining Balance
Total Loan
Back to home
log Out


Developped By Quentin MIDY - 2018
Icons taken from flaticon.com - under Flaticon Basic License - Published by Freepik
Cover picture taken from https://www.pexels.com/photo/crowd-watching-show-inside-the-dark-stadium-761543/ - under CC0 License - Published by Jack Gittoes


Favorited by: {{ recipe.favorited_by }} {{ recipe.name }} Edit
Recipe time: {{ recipe.cook_time }}
Recipe description: {{ recipe.description }}


Boris Johnson’s favourite band is The Clash – and fans are not happy about it
The PM also said he listens to The Rolling Stones
Boris Johnson has received a backlash for declaring that he’s a fan of The Clash.
The revelation came from a new general election campaign video in which the Prime Minister is seen walking around the Conservative Party headquarters answering questions.
At one point he is asked who his favourite band is and he replies: “Look this is either The Clash or The Rolling Stones, and mainly I listen to The Rolling Stones nowadays, so you can make of that what you will.”
Fans of The Clash were quick to air their ire on Twitter concerning the Prime Minister’s comments. “David Cameron liked The Jam, Boris Johnson likes The Clash. Do any of these chinless fucks even listen to the lyrics. Next Jacob Rees Mogg will be telling us how he loves NWA and was always down with the west coast vibe,” one wrote, while another added: “Don’t pretend to like the Clash, you lying Tory fuckbrain.”
You can view a selection of further responses below.
One fan did defend the Johnson’s choices, pointing out that he did previously once choose The Clash song ‘Pressure Drop’ and ‘Start Me Up’ by The Rolling Stones on Desert Island Discs in 2005.
The surviving members of The Clash are yet comment on Johnson’s remarks but NME is chasing for a response.
David Cameron sparked similar outrage nearly a decade ago when he said he was a fan of The Smiths. In 2010, The Smiths’ guitarist Johnny Marr tweeted: “David Cameron, stop saying that you like The Smiths, no you don’t. I forbid you to like it.”
Marr also recently slammed those who kept referring to Johnson by his first name like “some cuddly fun character”. “I wish people would stop referring to ‘Boris’ like he’s some cuddly fun character. They should refer to him by his full name; ‘That Wanker Boris Johnson'”, he added.
Meanwhile, Noel Gallagher recently conceded that he’d rather have Johnson than Liam for a brother.
“I would say Boris is more entertaining,” Noel told The Daily Star. “His use of the English language is more superior.”
However, he was willing to admit that Liam would emerge triumphant in the beauty stakes.
“Liam is better looking though,” he said. “I probably would not get on with either of them.”


Awareness Precipitates from Order Out Of Chaos
Under what circumstances does order emerge from chaos? Does it always present with stratification and interwoven hierarchical self-similarity? When do the fractal features begin to react to themselves, reflecting their own images back into themselves? This is what leads to higher levels of order in chaos. If chaotic systems yield order that compels some form of ergodicity to emerge, is it truly chaotic?
International Trends 2020: The Automation Crisis
Artificial intelligence, fabriction and other technology drive unemployment. High rates of unemployment drastically lower median income in developed nations. These economies have higher debt saturation on consumers, which ostensibly enables faster growth, but this dependency on already established revenue streams leads to greater surface area for systemic risk. These higher levels of debt saturation lead to more severely constricted liquidity in situations of lowered employment. The lost liquidity leads to fewer new investments and less capability to develop economic opportunities to rise oneself out of crisis.
International Trends 2020: Universal Basic Income
Economic growth ultimately stems from the net contributions of individuals. It's built from the ground up. We know that we are going to have dozens of millions of unemployed between ages 20 and 60 by the 2030's. The point is to invest that human potential and manpower to get the greatest return possible in anticipation of greater future threats to human existance. More challenging than the operational aspects is convincing Americans that this is not only necessary, but should be enthusiastically embraced when technology seems to remove most constraints. To do this we need a cultural transformation to produce a society built on values and character with a strong sense of identity and duty.
Harnessing the Congruence of the Human Condition for Natural Justice
So, if through knowledge people align their energy, which is their individual capacity to change their local circumstances, our collective capacity to change the world is magnified in proportion greater than the number of people who come together. As we continue fighting each other in diametric opposition, we only cause ourselves to become vulnerable to subversion. Yet, if we decide to move forward together, then the restraints of injustice become like gossamer chains and are only as strong as the remnants of collective delusion...
International Trends 2020: The Smart Grid
Researchers across the world are revitalizing their interests in power grid technology and solving many electrical engineering problems that otherwise lay dormant for decades. To Cisco certified networking enthusiasts such as myself, one particularly interesting area of smart grid research is power packet routing. To the layman, this essentially combines the internet and electric power distribution, so your devices can be connected to the internet by simply being plugged in. This helps IoT devices quite a bit.
International Trends 2020: Climate Change
Our world does not need to deal with billions of hungry people. Instead humanity needs to ensure every last person on the planet is fully enabled to contribute their maximum potential because we need every one. With optimal contribution of net human potential, overpopulation doesn't burden us. It instead empowers us to reach our full potential.
The Turing Network: A Thought Experiment for Quantum Computing
Imagine your standard Turing Machine, but something a bit different. Instead of maintaining program state in the a tape with discretized values, this Turing Network instead processes waveforms where state can be encoded in various ways, including in spectral transformations. And this is a network, not a simple machine, where state is distributed amongst various autonomous Turing Machines.
Civil Disobedience and the Operational Level of Information Warfare
Today, we are approaching a world with unprecedented sociocultural dynamics that have never been part of the paradigm of secrecy in any era until tomorrow's. Since the epoch before commerce and discovery of metallurgy, the incentive to keep information secret has pervaded culture, even resulting in cultural movements such as esotericism. That prevailing paradigm of secrecy, often relegated to the background of human culture, has in recent years eluded the need for close inspection.
Oneirontology: Engineering Cultural Touchstones for Mythos
How does one become familiar with different systems of knowledge and culture perpetuation? Like Merlin and the druids of Celt, one accrues this knowledge over time, by learning to weave ideas and their semiotic pointers.
Oneirontology: Semiotics, Karma and Moral Consequentialism
There is a limitless, self-magnifying source of power that any lifeform in the universe can tap in to. This power is encoded into the invisible metaversal leylines that lay buried under mappings of semiotic networks. Humanity sees these semiotic networks rise into the visible planes through culture, which is always invisibly mapped to the same aeternal flames. Through these leylines, humanity can retrieve power that transcends time itself. This power can be used for good or for evil, but by closely guarding it, We can ensure that its use fertilizes the soil of culture, eventually sprouting heroism and virtue whereever there is enough light and water. Then, We can use these leylines to reify a kind of penetrating light that chokes evil by starving its supply of darkness.


{% extends "blog/layout.html" %} {% block content %}
This is a sample blog written with Python, Django and Javascript, developed by Aline Souza.


Basic Steps of Scientific Investigations¶
An overarching aim in this course is to give you a deeper understanding of the scientific method. The problems we study will all involve cases where we can apply classical mechanics. In our previous material we already assumed that we had a model for the motion of an object. Alternatively we could have data from experiment (like Usain Bolt’s 100m world record run in 2008). Or we could have performed ourselves an experiment and we want to understand which forces are at play and whether these forces can be understood in terms of fundamental forces.
Our first step consists in identifying the problem. What we sketch here may include a mix of experiment and theoretical simulations, or just experiment or only theory.
Identifying our System¶
Here we can ask questions like
What kind of object is moving
What kind of data do we have
How do we measure position, velocity, acceleration etc
Which initial conditions influence our system
Other aspects which allow us to identify the system
Defining a Model¶
With our eventual data and observations we would now like to develop a model for the system. In the end we want obviously to be able to understand which forces are at play and how they influence our specific system. That is, can we extract some deeper insights about a system?
We need then to
Find the forces that act on our system
Introduce models for the forces
Identify the equations which can govern the system (Newton’s second law for example)
More elements we deem important for defining our model
Solving the Equations¶
With the model at hand, we can then solve the equations. In classical mechanics we normally end up with solving sets of coupled ordinary differential equations or partial differential equations.
Using Newton’s second law we have equations of the type \(\boldsymbol{F}=m\boldsymbol{a}=md\boldsymbol{v}/dt\)
We need to define the initial conditions (typically the initial velocity and position as functions of time) and/or initial conditions and boundary conditions
The solution of the equations give us then the position, the velocity and other time-dependent quantities which may specify the motion of a given object.
We are not yet done. With our lovely solvers, we need to start thinking.
Now it is time to ask the big questions. What do our results mean? Can we give a simple interpretation in terms of fundamental laws? What do our results mean? Are they correct? Thus, typical questions we may ask are
Are our results for say \(\boldsymbol{r}(t)\) valid? Do we trust what we did? Can you validate and verify the correctness of your results?
Evaluate the answers and their implications
Compare with experimental data if possible. Does our model make sense?
and obviously many other questions.
The analysis stage feeds back to the first stage. It may happen that the data we had were not good enough, there could be large statistical uncertainties. We may need to collect more data or perhaps we did a sloppy job in identifying the degrees of freedom.
All these steps are essential elements in a scientific enquiry. Hopefully, through a mix of numerical simulations, analytical calculations and experiments we may gain a deeper insight about the physics of a specific system.
Let us now remind ourselves of Newton’s laws, since these are the laws of motion we will study in this course.
Newton’s Laws¶
When analyzing a physical system we normally start with distinguishing between the object we are studying (we will label this in more general terms as our system) and how this system interacts with the environment (which often means everything else!)
In our investigations we will thus analyze a specific physics problem in terms of the system and the environment. In doing so we need to identify the forces that act on the system and assume that the forces acting on the system must have a source, an identifiable cause in the environment.
A force acting on for example a falling object must be related to an interaction with something in the environment. This also means that we do not consider internal forces. The latter are forces between one part of the object and another part. In this course we will mainly focus on external forces.
Forces are either contact forces or long-range forces.
Contact forces, as evident from the name, are forces that occur at the contact between the system and the environment. Well-known long-range forces are the gravitional force and the electromagnetic force.
Setting up a model for forces acting on an object¶
In order to set up the forces which act on an object, the following steps may be useful
Divide the problem into system and environment.
Draw a figure of the object and everything in contact with the object.
Draw a closed curve around the system.
Find contact points—these are the points where contact forces may act.
Give names and symbols to all the contact forces.
Identify the long-range forces.
Make a drawing of the object. Draw the forces as arrows, vectors, starting from where the force is acting. The direction of the vector(s) indicates the (positive) direction of the force. Try to make the length of the arrow indicate the relative magnitude of the forces.
Draw in the axes of the coordinate system. It is often convenient to make one axis parallel to the direction of motion. When you choose the direction of the axis you also choose the positive direction for the axis.
Newton’s Laws, the Second one first¶
Newton’s second law of motion: The force \(\boldsymbol{F}\) on an object of inertial mass \(m\) is related to the acceleration a of the object through
where \(\boldsymbol{a}\) is the acceleration.
Newton’s laws of motion are laws of nature that have been found by experimental investigations and have been shown to hold up to continued experimental investigations. Newton’s laws are valid over a wide range of length- and time-scales. We use Newton’s laws of motion to describe everything from the motion of atoms to the motion of galaxies.
The second law is a vector equation with the acceleration having the same direction as the force. The acceleration is proportional to the force via the mass \(m\) of the system under study.
Newton’s second law introduces a new property of an object, the so-called inertial mass \(m\). We determine the inertial mass of an object by measuring the acceleration for a given applied force.
Then the First Law¶
What happens if the net external force on a body is zero? Applying Newton’s second law, we find:
which gives using the definition of the acceleration
The acceleration is zero, which means that the velocity of the object is constant. This is often referred to as Newton’s first law. An object in a state of uniform motion tends to remain in that state unless an external force changes its state of motion. Why do we need a separate law for this? Is it not simply a special case of Newton’s second law? Yes, Newton’s first law can be deduced from the second law as we have illustrated. However, the first law is often used for a different purpose: Newton’s First Law tells us about the limit of applicability of Newton’s Second law. Newton’s Second law can only be used in reference systems where the First law is obeyed. But is not the First law always valid? No! The First law is only valid in reference systems that are not accelerated. If you observe the motion of a ball from an accelerating car, the ball will appear to accelerate even if there are no forces acting on it. We call systems that are not accelerating inertial systems, and Newton’s first law is often called the law of inertia. Newton’s first and second laws of motion are only valid in inertial systems.
A system is an inertial system if it is not accelerated. It means that the reference system must not be accelerating linearly or rotating. Unfortunately, this means that most systems we know are not really inertial systems. For example, the surface of the Earth is clearly not an inertial system, because the Earth is rotating. The Earth is also not an inertial system, because it ismoving in a curved path around the Sun. However, even if the surface of the Earth is not strictly an inertial system, it may be considered to be approximately an inertial system for many laboratory-size experiments.
And finally the Third Law¶
If there is a force from object A on object B, there is also a force from object B on object A. This fundamental principle of interactions is called Newton’s third law. We do not know of any force that do not obey this law: All forces appear in pairs. Newton’s third law is usually formulated as: For every action there is an equal and opposite reaction.
Motion of a Single Object¶
Here we consider the motion of a single particle moving under the influence of some set of forces. We will consider some problems where the force does not depend on the position. In that case Newton’s law \(m\dot{\boldsymbol{v}}=\boldsymbol{F}(\boldsymbol{v})\) is a first-order differential equation and one solves for \(\boldsymbol{v}(t)\), then moves on to integrate \(\boldsymbol{v}\) to get the position. In essentially all of these cases we cna find an analytical solution.
Air Resistance in One Dimension¶
Air resistance tends to scale as the square of the velocity. This is in contrast to many problems chosen for textbooks, where it is linear in the velocity. The choice of a linear dependence is motivated by mathematical simplicity (it keeps the differential equation linear) rather than by physics. One can see that the force should be quadratic in velocity by considering the momentum imparted on the air molecules. If an object sweeps through a volume \(dV\) of air in time \(dt\), the momentum imparted on the air is
where \(v\) is the velocity of the object and \(\rho_m\) is the mass density of the air. If the molecules bounce back as opposed to stop you would double the size of the term. The opposite value of the momentum is imparted onto the object itself. Geometrically, the differential volume is
where \(A\) is the cross-sectional area and \(vdt\) is the distance the object moved in time \(dt\).
Resulting Acceleration¶
Plugging this into the expression above,
This is the force felt by the particle, and is opposite to its direction of motion. Now, because air doesn’t stop when it hits an object, but flows around the best it can, the actual force is reduced by a dimensionless factor \(c_W\), called the drag coefficient.
and the acceleration is
For a particle with initial velocity \(v_0\), one can separate the \(dt\) to one side of the equation, and move everything with \(v\)s to the other side. We did this in our discussion of simple motion and will not repeat it here.
On more general terms, for many systems, e.g. an automobile, there are multiple sources of resistance. In addition to wind resistance, where the force is proportional to \(v^2\), there are dissipative effects of the tires on the pavement, and in the axel and drive train. These other forces can have components that scale proportional to \(v\), and components that are independent of \(v\). Those independent of \(v\), e.g. the usual \(f=\mu_K N\) frictional force you consider in your first Physics courses, only set in once the object is actually moving. As speeds become higher, the \(v^2\) components begin to dominate relative to the others. For automobiles at freeway speeds, the \(v^2\) terms are largely responsible for the loss of efficiency. To travel a distance \(L\) at fixed speed \(v\), the energy/work required to overcome the dissipative forces are \(fL\), which for a force of the form \(f=\alpha v^n\) becomes
For \(n=0\) the work is independent of speed, but for the wind resistance, where \(n=2\), slowing down is essential if one wishes to reduce fuel consumption. It is also important to consider that engines are designed to be most efficient at a chosen range of power output. Thus, some cars will get better mileage at higher speeds (They perform better at 50 mph than at 5 mph) despite the considerations mentioned above.
Going Ballistic, Projectile Motion or a Softer Approach, Falling Raindrops¶
As an example of Newton’s Laws we consider projectile motion (or a falling raindrop or a ball we throw up in the air) with a drag force. Even though air resistance is largely proportional to the square of the velocity, we will consider the drag force to be linear to the velocity, \(\boldsymbol{F}=-m\gamma\boldsymbol{v}\), for the purposes of this exercise. The acceleration for a projectile moving upwards, \(\boldsymbol{a}=\boldsymbol{F}/m\), becomes
and \(\gamma\) has dimensions of inverse time.
If you on the other hand have a falling raindrop, how do these equations change? See for example Figure 2.1 in Taylor. Let us stay with a ball which is thrown up in the air at \(t=0\).
Ways of solving these equations¶
We will go over two different ways to solve this equation. The first by direct integration, and the second as a differential equation. To do this by direct integration, one simply multiplies both sides of the equations above by \(dt\), then divide by the appropriate factors so that the \(v\)s are all on one side of the equation and the \(dt\) is on the other. For the \(x\) motion one finds an easily integrable equation,
This is very much the result you would have written down by inspection. For the \(y\)-component of the velocity,
Whereas \(v_x\) starts at some value and decays exponentially to zero, \(v_y\) decays exponentially to the terminal velocity, \(v_t=-g/\gamma\).
Solving as differential equations¶
Although this direct integration is simpler than the method we invoke below, the method below will come in useful for some slightly more difficult differential equations in the future. The differential equation for \(v_x\) is straight-forward to solve. Because it is first order there is one arbitrary constant, \(A\), and by inspection the solution is
The arbitrary constants for equations of motion are usually determined by the initial conditions, or more generally boundary conditions. By inspection \(A=v_{0x}\), the initial \(x\) component of the velocity.
Differential Equations, contn¶
The differential equation for \(v_y\) is a bit more complicated due to the presence of \(g\). Differential equations where all the terms are linearly proportional to a function, in this case \(v_y\), or to derivatives of the function, e.g., \(v_y\), \(dv_y/dt\), \(d^2v_y/dt^2\cdots\), are called linear differential equations. If there are terms proportional to \(v^2\), as would happen if the drag force were proportional to the square of the velocity, the differential equation is not longer linear. Because this expression has only one derivative in \(v\) it is a first-order linear differential equation. If a term were added proportional to \(d^2v/dt^2\) it would be a second-order differential equation. In this case we have a term completely independent of \(v\), the gravitational acceleration \(g\), and the usual strategy is to first rewrite the equation with all the linear terms on one side of the equal sign,
Splitting into two parts¶
Now, the solution to the equation can be broken into two parts. Because this is a first-order differential equation we know that there will be one arbitrary constant. Physically, the arbitrary constant will be determined by setting the initial velocity, though it could be determined by setting the velocity at any given time. Like most differential equations, solutions are not “solved”. Instead, one guesses at a form, then shows the guess is correct. For these types of equations, one first tries to find a single solution, i.e. one with no arbitrary constants. This is called the {\it particular} solution, \(y_p(t)\), though it should really be called “a” particular solution because there are an infinite number of such solutions. One then finds a solution to the {\it homogenous} equation, which is the equation with zero on the right-hand side,
Homogenous solutions will have arbitrary constants.
The particular solution will solve the same equation as the original general equation
However, we don’t need find one with arbitrary constants. Hence, it is called a particular solution.
The sum of the two,
is a solution of the total equation because of the linear nature of the differential equation. One has now found a general solution encompassing all solutions, because it both satisfies the general equation (like the particular solution), and has an arbitrary constant that can be adjusted to fit any initial condition (like the homogneous solution). If the equation were not linear, e.g if there were a term such as \(v_y^2\) or \(v_y\dot{v}_y\), this technique would not work.
More details¶
Returning to the example above, the homogenous solution is the same as that for \(v_x\), because there was no gravitational acceleration in that case,
In this case a particular solution is one with constant velocity,
Note that this is the terminal velocity of a particle falling from a great height. The general solution is thus,
and one can find \(B\) from the initial velocity,
Plugging in the expression for \(B\) gives the \(y\) motion given the initial velocity,
It is easy to see that this solution has \(v_y=v_{0y}\) when \(t=0\) and \(v_y=-g/\gamma\) when \(t\rightarrow\infty\).
One can also integrate the two equations to find the coordinates \(x\) and \(y\) as functions of \(t\),
If the question was to find the position at a time \(t\), we would be finished. However, the more common goal in a projectile equation problem is to find the range, i.e. the distance \(x\) at which \(y\) returns to zero. For the case without a drag force this was much simpler. The solution for the \(y\) coordinate would have been \(y=v_{0y}t-gt^2/2\). One would solve for \(t\) to make \(y=0\), which would be \(t=2v_{0y}/g\), then plug that value for \(t\) into \(x=v_{0x}t\) to find \(x=2v_{0x}v_{0y}/g=v_0\sin(2\theta_0)/g\). One follows the same steps here, except that the expression for \(y(t)\) is more complicated. Searching for the time where \(y=0\), and we get
This cannot be inverted into a simple expression \(t=\cdots\). Such expressions are known as “transcendental equations”, and are not the rare instance, but are the norm. In the days before computers, one might plot the right-hand side of the above graphically as a function of time, then find the point where it crosses zero.
Now, the most common way to solve for an equation of the above type would be to apply Newton’s method numerically. This involves the following algorithm for finding solutions of some equation \(F(t)=0\).
First guess a value for the time, \(t_{\rm guess}\).
Calculate \(F\) and its derivative, \(F(t_{\rm guess})\) and \(F'(t_{\rm guess})\).
Unless you guessed perfectly, \(F\ne 0\), and assuming that \(\Delta F\approx F'\Delta t\), one would choose
\(\Delta t=-F(t_{\rm guess})/F'(t_{\rm guess})\).
Now repeat step 1, but with \(t_{\rm guess}\rightarrow t_{\rm guess}+\Delta t\).
If the \(F(t)\) were perfectly linear in \(t\), one would find \(t\) in one step. Instead, one typically finds a value of \(t\) that is closer to the final answer than \(t_{\rm guess}\). One breaks the loop once one finds \(F\) within some acceptable tolerance of zero. A program to do this will be added shortly.
Motion in a Magnetic Field¶
Another example of a velocity-dependent force is magnetism,
For a uniform field in the \(z\) direction \(\boldsymbol{B}=B\hat{z}\), the force can only have \(x\) and \(y\) components,
The differential equations are
One can solve the equations by taking time derivatives of either equation, then substituting into the other equation,
The solution to these equations can be seen by inspection,
One can integrate the equations to find the positions as a function of time,
The trajectory is a circle centered at \(x_0,y_0\) with amplitude \(A\) rotating in the clockwise direction.
The equations of motion for the \(z\) motion are
which leads to
Added onto the circle, the motion is helical.
Note that the kinetic energy,
is constant. This is because the force is perpendicular to the velocity, so that in any differential time element \(dt\) the work done on the particle \(\boldsymbol{F}\cdot{dr}=dt\boldsymbol{F}\cdot{v}=0\).
One should think about the implications of a velocity dependent force. Suppose one had a constant magnetic field in deep space. If a particle came through with velocity \(v_0\), it would undergo cyclotron motion with radius \(R=v_0/\omega_c\). However, if it were still its motion would remain fixed. Now, suppose an observer looked at the particle in one reference frame where the particle was moving, then changed their velocity so that the particle’s velocity appeared to be zero. The motion would change from circular to fixed. Is this possible?
The solution to the puzzle above relies on understanding relativity. Imagine that the first observer believes \(\boldsymbol{B}\ne 0\) and that the electric field \(\boldsymbol{E}=0\). If the observer then changes reference frames by accelerating to a velocity \(\boldsymbol{v}\), in the new frame \(\boldsymbol{B}\) and \(\boldsymbol{E}\) both change. If the observer moved to the frame where the charge, originally moving with a small velocity \(v\), is now at rest, the new electric field is indeed \(\boldsymbol{v}\times\boldsymbol{B}\), which then leads to the same acceleration as one had before. If the velocity is not small compared to the speed of light, additional \(\gamma\) factors come into play, \(\gamma=1/\sqrt{1-(v/c)^2}\). Relativistic motion will not be considered in this course.
Sliding Block tied to a Wall¶
Another classical case is that of simple harmonic oscillations, here represented by a block sliding on a horizontal frictionless surface. The block is tied to a wall with a spring. If the spring is not compressed or stretched too far, the force on the block at a given position \(x\) is
The negative sign means that the force acts to restore the object to an equilibrium position. Newton’s equation of motion for this idealized system is then
or we could rephrase it as
with the angular frequency \(\omega_0^2=k/m\).
The above differential equation has the advantage that it can be solved analytically with solutions on the form
where \(A\) is the amplitude and \(\nu\) the phase constant. This provides in turn an important test for the numerical solution and the development of a program for more complicated cases which cannot be solved analytically.
With the position \(x(t)\) and the velocity \(v(t)=dx/dt\) we can reformulate Newton’s equation in the following way
and
We are now going to solve these equations using first the standard forward Euler method. Later we will try to improve upon this.
Before proceeding however, it is important to note that in addition to the exact solution, we have at least two further tests which can be used to check our solution.
Since functions like \(cos\) are periodic with a period \(2\pi\), then the solution \(x(t)\) has also to be periodic. This means that
with \(T\) the period defined as
Observe that \(T\) depends only on \(k/m\) and not on the amplitude of the solution.
In addition to the periodicity test, the total energy has also to be conserved.
Suppose we choose the initial conditions
meaning that block is at rest at \(t=0\) but with a potential energy
The total energy at any time \(t\) has however to be conserved, meaning that our solution has to fulfil the condition
We will derive this equation in our discussion on energy conservation.
An algorithm which implements these equations is included below.
Choose the initial position and speed, with the most common choice \(v(t=0)=0\) and some fixed value for the position.
Choose the method you wish to employ in solving the problem.
Subdivide the time interval \([t_i,t_f] \) into a grid with step size
where \(N\) is the number of mesh points.
Calculate now the total energy given by
Choose ODE solver to obtain \(x_{i+1}\) and \(v_{i+1}\) starting from the previous values \(x_i\) and \(v_i\).
When we have computed \(x(v)_{i+1}\) we upgrade \(t_{i+1}=t_i+h\).
This iterative process continues till we reach the maximum time \(t_f\).
The results are checked against the exact solution. Furthermore, one has to check the stability of the numerical solution against the chosen number of mesh points \(N\).
The following python program ( code will be added shortly)
#
# This program solves Newtons equation for a block sliding on
# an horizontal frictionless surface.
# The block is tied to the wall with a spring, so N's eq takes the form:
#
# m d^2x/dt^2 = - kx
#
# In order to make the solution dimless, we set k/m = 1.
# This results in two coupled diff. eq's that may be written as:
#
# dx/dt = v
# dv/dt = -x
#
# The user has to specify the initial velocity and position,
# and the number of steps. The time interval is fixed to
# t \in [0, 4\pi) (two periods)
#
The classical pendulum and scaling the equations¶
The angular equation of motion of the pendulum is given by Newton’s equation and with no external force it reads
with an angular velocity and acceleration given by
and
More on the Pendulum¶
We do however expect that the motion will gradually come to an end due a viscous drag torque acting on the pendulum. In the presence of the drag, the above equation becomes
where \(\nu\) is now a positive constant parameterizing the viscosity of the medium in question. In order to maintain the motion against viscosity, it is necessary to add some external driving force. We choose here a periodic driving force. The last equation becomes then
with \(A\) and \(\omega\) two constants representing the amplitude and the angular frequency respectively. The latter is called the driving frequency.
More on the Pendulum¶
We define
the so-called natural frequency and the new dimensionless quantities
with the dimensionless driving frequency
and introducing the quantity \(Q\), called the quality factor,
and the dimensionless amplitude
We have
This equation can in turn be recast in terms of two coupled first-order differential equations as follows
and
These are the equations to be solved. The factor \(Q\) represents the number of oscillations of the undriven system that must occur before its energy is significantly reduced due to the viscous drag. The amplitude \(\hat{A}\) is measured in units of the maximum possible gravitational torque while \(\hat{\omega}\) is the angular frequency of the external torque measured in units of the pendulum’s natural frequency.