`); let searchUrl = `/search/`; history.forEach((elem) => { prevsearch.find('#prevsearch-options').append(`
${elem} `); }); } $('#search-pretype-options').empty(); $('#search-pretype-options').append(prevsearch); let prevbooks = $(false); [ {title:"Recently Opened Textbooks", books:previous_books}, {title:"Recommended Textbooks", books:recommended_books} ].forEach((book_segment) => { if (Array.isArray(book_segment.books) && book_segment.books.length>0 && nsegments<2) { nsegments+=1; prevbooks = $(`
${book_segment.title} `); let searchUrl = "/books/xxx/"; book_segment.books.forEach((elem) => { prevbooks.find('#prevbooks-options'+nsegments.toString()).append(`
${elem.title} ${ordinal(elem.edition)} ${elem.author} `); }); } $('#search-pretype-options').append(prevbooks); }); } function anon_pretype() { let prebooks = null; try { prebooks = JSON.parse(localStorage.getItem('PRETYPE_BOOKS_ANON')); }catch(e) {} if ('previous_books' in prebooks && 'recommended_books' in prebooks) { previous_books = prebooks.previous_books; recommended_books = prebooks.recommended_books; if (typeof PREVBOOKS !== 'undefined' && Array.isArray(PREVBOOKS)) { new_prevbooks = PREVBOOKS; previous_books.forEach(elem => { for (let i = 0; i < new_prevbooks.length; i++) { if (elem.id == new_prevbooks[i].id) { return; } } new_prevbooks.push(elem); }); new_prevbooks = new_prevbooks.slice(0,3); previous_books = new_prevbooks; } if (typeof RECBOOKS !== 'undefined' && Array.isArray(RECBOOKS)) { new_recbooks = RECBOOKS; for (let j = 0; j < new_recbooks.length; j++) { new_recbooks[j].viewed_at = new Date(); } let insert = true; for (let i=0; i < recommended_books.length; i++){ for (let j = 0; j < new_recbooks.length; j++) { if (recommended_books[i].id == new_recbooks[j].id) { insert = false; } } if (insert){ new_recbooks.push(recommended_books[i]); } } new_recbooks.sort((a,b)=>{ adate = new Date(2000, 0, 1); bdate = new Date(2000, 0, 1); if ('viewed_at' in a) {adate = new Date(a.viewed_at);} if ('viewed_at' in b) {bdate = new Date(b.viewed_at);} // 100000000: instead of just erasing the suggestions from previous week, // we just move them to the back of the queue acurweek = ((new Date()).getDate()-adate.getDate()>7)?0:100000000; bcurweek = ((new Date()).getDate()-bdate.getDate()>7)?0:100000000; aviews = 0; bviews = 0; if ('views' in a) {aviews = acurweek+a.views;} if ('views' in b) {bviews = bcurweek+b.views;} return bviews - aviews; }); new_recbooks = new_recbooks.slice(0,3); recommended_books = new_recbooks; } localStorage.setItem('PRETYPE_BOOKS_ANON', JSON.stringify({ previous_books: previous_books, recommended_books: recommended_books })); build_popup(); } } var whiletyping_search_object = null; var whiletyping_search = { books: [], curriculum: [], topics: [] } var single_whiletyping_ajax_promise = null; var whiletyping_database_initial_burst = 0; //number of consecutive calls, after 3 we start the 1 per 5 min calls function get_whiletyping_database() { //gets the database from the server. // 1. by validating against a local database value we confirm that the framework is working and // reduce the ammount of continuous calls produced by errors to 1 per 5 minutes. return localforage.getItem('whiletyping_last_attempt').then(function(value) { if ( value==null || (new Date()) - (new Date(value)) > 1000*60*5 || (whiletyping_database_initial_burst < 3) ) { localforage.setItem('whiletyping_last_attempt', (new Date()).getTime()); // 2. Make an ajax call to the server and get the search database. let databaseUrl = `/search/whiletype_database/`; let resp = single_whiletyping_ajax_promise; if (resp === null) { whiletyping_database_initial_burst = whiletyping_database_initial_burst + 1; single_whiletyping_ajax_promise = resp = new Promise((resolve, reject) => { $.ajax({ url: databaseUrl, type: 'POST', data:{csrfmiddlewaretoken: "UxkyiBUv2FwzTq0VWL2mHa9yxWTRgLyoK8RrYedOEsxFVPFUmWqSnbq3Kzmy5sqJ"}, success: function (data) { // 3. verify that the elements of the database exist and are arrays if ( ('books' in data) && ('curriculum' in data) && ('topics' in data) && Array.isArray(data.books) && Array.isArray(data.curriculum) && Array.isArray(data.topics)) { localforage.setItem('whiletyping_last_success', (new Date()).getTime()); localforage.setItem('whiletyping_database', data); resolve(data); } }, error: function (error) { console.log(error); resolve(null); }, complete: function (data) { single_whiletyping_ajax_promise = null; } }) }); } return resp; } return Promise.resolve(null); }).catch(function(err) { console.log(err); return Promise.resolve(null); }); } function get_whiletyping_search_object() { // gets the fuse objects that will be in charge of the search if (whiletyping_search_object){ return Promise.resolve(whiletyping_search_object); } database_promise = localforage.getItem('whiletyping_database').then(function(database) { return localforage.getItem('whiletyping_last_success').then(function(last_success) { if (database==null || (new Date()) - (new Date(last_success)) > 1000*60*60*24*30 || (new Date('2023-04-25T00:00:00')) - (new Date(last_success)) > 0) { // New database update return get_whiletyping_database().then(function(new_database) { if (new_database) { database = new_database; } return database; }); } else { return Promise.resolve(database); } }); }); return database_promise.then(function(database) { if (database) { const options = { isCaseSensitive: false, includeScore: true, shouldSort: true, // includeMatches: false, // findAllMatches: false, // minMatchCharLength: 1, // location: 0, threshold: 0.2, // distance: 100, // useExtendedSearch: false, ignoreLocation: true, // ignoreFieldNorm: false, // fieldNormWeight: 1, keys: [ "title" ] }; let curriculum_index={}; let topics_index={}; database.curriculum.forEach(c => curriculum_index[c.id]=c); database.topics.forEach(t => topics_index[t.id]=t); for (j=0; j
Solutions
Textbooks
`); } function build_solutions() { if (Array.isArray(solution_search_result)) { const viewAllHTML = userSubscribed ? `View All` : ''; var solutions_section = $(` Solutions ${viewAllHTML} `); let questionUrl = "/questions/xxx/"; let askUrl = "/ask/question/xxx/"; solution_search_result.forEach((elem) => { let url = ('course' in elem)?askUrl:questionUrl; let solution_type = ('course' in elem)?'ask':'question'; let subtitle = ('course' in elem)?(elem.course??""):(elem.book ?? "")+" "+(elem.chapter?"Chapter "+elem.chapter:""); solutions_section.find('#whiletyping-solutions').append(` ${elem.text} ${subtitle} `); }); $('#search-solution-options').empty(); if (Array.isArray(solution_search_result) && solution_search_result.length>0){ $('#search-solution-options').append(solutions_section); } MathJax.typesetPromise([document.getElementById('search-solution-options')]); } } function build_textbooks() { $('#search-pretype-options').empty(); $('#search-pretype-options').append($('#search-solution-options').html()); if (Array.isArray(textbook_search_result)) { var books_section = $(` Textbooks View All `); let searchUrl = "/books/xxx/"; textbook_search_result.forEach((elem) => { books_section.find('#whiletyping-books').append(` ${elem.title} ${ordinal(elem.edition)} ${elem.author} `); }); } if (Array.isArray(textbook_search_result) && textbook_search_result.length>0){ $('#search-pretype-options').append(books_section); } } function build_popup(first_time = false) { if ($('#search-text').val()=='') { build_pretype(); } else { solution_and_textbook_search(); } } var search_text_out = true; var search_popup_out = true; const is_login = false; const user_hash = null; function pretype_setup() { $('#search-text').focusin(function() { $('#search-popup').addClass('show'); resize_popup(); search_text_out = false; }); $( window ).resize(function() { resize_popup(); }); $('#search-text').focusout(() => { search_text_out = true; if (search_text_out && search_popup_out) { $('#search-popup').removeClass('show'); } }); $('#search-popup').mouseenter(() => { search_popup_out = false; }); $('#search-popup').mouseleave(() => { search_popup_out = true; if (search_text_out && search_popup_out) { $('#search-popup').removeClass('show'); } }); $('#search-text').on("keyup", delay(() => { build_popup(); }, 200)); build_popup(true); let prevbookUrl = `/search/pretype_books/`; let prebooks = null; try { prebooks = JSON.parse(localStorage.getItem('PRETYPE_BOOKS_'+(is_login?user_hash:'ANON'))); }catch(e) {} if (prebooks && 'previous_books' in prebooks && 'recommended_books' in prebooks) { if (is_login) { previous_books = prebooks.previous_books; recommended_books = prebooks.recommended_books; if (prebooks.time && new Date().getTime()-prebooks.time<1000*60*60*6) { build_popup(); return; } } else { anon_pretype(); return; } } $.ajax({ url: prevbookUrl, method: 'POST', data:{csrfmiddlewaretoken: "UxkyiBUv2FwzTq0VWL2mHa9yxWTRgLyoK8RrYedOEsxFVPFUmWqSnbq3Kzmy5sqJ"}, success: function(response){ previous_books = response.previous_books; recommended_books = response.recommended_books; if (is_login) { localStorage.setItem('PRETYPE_BOOKS_'+user_hash, JSON.stringify({ previous_books: previous_books, recommended_books: recommended_books, time: new Date().getTime() })); } build_popup(); }, error: function(response){ console.log(response); } }); } $( document ).ready(pretype_setup); $( document ).ready(function(){ $('#search-popup').on('click', '.search-view-item', function(e) { e.preventDefault(); let autoCompleteSearchViewUrl = `/search/autocomplete_search_view/`; let objectUrl = $(this).attr('href'); let selectedId = $(this).data('objid'); let searchResults = []; $("#whiletyping-solutions").find("a").each(function() { let is_selected = selectedId === $(this).data('objid'); searchResults.push({ objectId: $(this).data('objid'), contentType: $(this).data('contenttype'), category: $(this).data('category'), selected: is_selected }); }); $("#whiletyping-books").find("a").each(function() { let is_selected = selectedId === $(this).data('objid'); searchResults.push({ objectId: $(this).data('objid'), contentType: $(this).data('contenttype'), category: $(this).data('category'), selected: is_selected }); }); $.ajax({ url: autoCompleteSearchViewUrl, method: 'POST', data:{ csrfmiddlewaretoken: "UxkyiBUv2FwzTq0VWL2mHa9yxWTRgLyoK8RrYedOEsxFVPFUmWqSnbq3Kzmy5sqJ", query: $('#search-text').val(), searchObjects: JSON.stringify(searchResults) }, dataType: 'json', complete: function(data){ window.location.href = objectUrl; } }); }); });
FAQs
The Mass-Spring-Damper model is one of the most common models used by engineers to model kinematic systems. From human tissue to bridges, this straightforward model features three mechanisms and can be summarized as the following second-order differential equation: mx + c ˙x + kx = g(x, ˙x, t).
What is the mass spring equation for damping? ›
2: For a mass on a spring oscillating in a viscous fluid, the period remains constant, but the amplitudes of the oscillations decrease due to the damping caused by the fluid. ma=−bv−kx. md2xdt2+bdxdt+kx=0.
What is the equation for the forced mass-spring-damper model? ›
Spring-mass-damper theory applies the basic physics of F=ma to define suspension motion and response on bump impacts. Force (F) acting on the suspension is the combination of spring plus damping force. Mass (m) is the chassis or wheel weight depending on which body you want to look at.
What is the formula for a spring? ›
F = -kx. The proportional constant k is called the spring constant. It is a measure of the spring's stiffness. When a spring is stretched or compressed, so that its length changes by an amount x from its equilibrium length, then it exerts a force F = -kx in a direction towards its equilibrium position.
What is the formula for the damping system? ›
For a damped system, the equation of motion is a second order differential equation. This equation includes the acceleration, velocity, and position of a system with the expression d^2x/dt^2 + (c/m)dx/dt + (k/m)x = 0. The formula for a damped frequency comes from the coefficient of the velocity term.
What is the equation for a damper? ›
The equation for the force or moment produced by the damper, in either x or θ, is: →Fc=c→˙x, →Mc=c→˙θ, where c is the damping constant.
How to calculate damping coefficient? ›
The damping coefficient formula is an equation that represents the amount of energy dissipated by a damping system. It is typically denoted as "c" and can be calculated by dividing the damping force by the velocity of the object.
What is the formula for the damping ratio? ›
Using the natural frequency of a harmonic oscillator ω n = k m and the definition of the damping ratio above, we can rewrite this as: d 2 x d t 2 + 2 ζ ω n d x d t + ω n 2 x = 0. This equation can be solved with the approach. s = − ω n ( ζ ± i 1 − ζ 2 ) .
What is the formula for the mass spring system? ›
The equation for a spring-mass system can be stated as T=2√πm ⁄ k, it can be said that the time period varies directly with the mass. Ans. If a constant force (gravity in this case) is exerted on the mass, such that the force is collinear with the spring force, a simple harmonic motion will occur.
What is an example of a spring-mass-damper system? ›
2.2 Example second-order system: the spring-mass-damper system. Spring-mass-damper systems can be found in many mechanical systems. One common example is the suspension of a car. The car itself is the mass; it is suspended by an elastic spring.
The object of the car suspension is to decouple the motions of the wheels from those of the vehicle body. Bumps from the road surface that are transmitted to the car body via the wheels should be reduced to the minimum.
What is the formula for damping spring force? ›
I'm modelling particles in a system using a spring and damper force. x=xi−xf, where xi=centre of spring and xf= displaced position. Above x is the displacement and v is the velocity in the previous timestep.
What is the characteristic equation of a mass-spring-damper? ›
The characteristic equation is r2 + 5r + 4 = 0, so the roots are r = -1 and r = -4. The system is over damped. The max occurs at a horizontal tangent; set u'(t)= 0 and solve for t. Over damped.
What is the derivation of the spring-mass-damper system? ›
A spring mass damper system (mass m, stiffness k, and damping coefficient c) excited by a force F(t) = B sin ωt, where B, ω and t are the amplitude, frequency and time, respectively, is shown in the figure. Four different responses of the system (marked as (i) to (iv)) are shown just to the right of the system figure.
What is the governing equation for the mass spring damper model? ›
Question: The governing equation for a spring-mass-damper system is given by2x¨+3x˙+5x=F(t)where F(t) is an externally applied force. You can assume that the initial conditions are x(0)=0, and x˙(0)=0.1(a) Compute the transfer function for the system.
What is the formula for the damping ratio of a spring? ›
If we denote the damping coefficient as , the critical damping as c c r , the damping ratio can be defined as follows: ζ = c c c r Here are some things to consider: If , the system is underdamped. In this case, the system will oscillate, but the oscillations will die out over time. If , the system is critically damped.
What is the equation for the spring-mass vibration? ›
The equation of motion for a spring-mass system excited by a harmonic force is. M x ¨ + k x = F cos Where M is the mass, K is the spring stiffness, F is the force amplitude and ω is the angular frequency of excitation. Resonance occurs when ω is equal to.