Колебания груза на пружине
Материал из Department of Theoretical and Applied Mechanics
Задача: С помощью языка программирования JavaScript смоделировать колебания груза на пружине.
Содержание
Решение
Программа: скачать
Текст программы на языке JavaScript:
Файл "5.js"
1 function main()
2 {
3 var step = 0;
4 var rr = new THREE.WebGLRenderer();
5 rr.setSize(window.innerWidth, window.innerHeight);
6 rr.setClearColor(0xFFFFFFF,1);
7 document.body.appendChild(rr.domElement);
8 camera = new THREE.PerspectiveCamera(45, window.innerWidth / window.innerHeight, 1, 500);
9 camera.position.set(0, 0, 100);
10 camera.lookAt(new THREE.Vector3(0, 0, 0));
11 var scene = new THREE.Scene();
12
13 var material = new THREE.LineBasicMaterial({color: 0x000000});
14 var material1 = new THREE.LineBasicMaterial({color: 0xbbbbbb});
15
16 var radius = 5;
17 var segments = 32;
18
19 var circleGeometry = new THREE.CircleGeometry(radius, segments);
20 var circle = new THREE.Mesh(circleGeometry, material1);
21
22 var radius1 = 0.5;
23 var segments1 = 32;
24
25 var circleGeometry = new THREE.CircleGeometry(radius1, segments1);
26 var circle1 = new THREE.Mesh(circleGeometry, material);
27
28 var geometry = new THREE.Geometry();
29 geometry.vertices.push(new THREE.Vector3(-40, 20, 0));
30 geometry.vertices.push(new THREE.Vector3(0, 20, 0));
31
32 var line = new THREE.Line(geometry, material);
33 line.geometry.verticesNeedUpdate = true;
34 geometry.dynamic = true;
35
36 var geometry1 = new THREE.Geometry();
37 geometry1.vertices.push(new THREE.Vector3(-28, 28, 0));
38 geometry1.vertices.push(new THREE.Vector3(-28, 27, 0));
39
40 var line1 = new THREE.Line(geometry1, material);
41 line1.geometry.verticesNeedUpdate = true;
42 geometry1.dynamic = true;
43
44 var geometry2 = new THREE.Geometry();
45 geometry2.vertices.push(new THREE.Vector3(-30, 22, 0));
46 geometry2.vertices.push(new THREE.Vector3(-26, 21, 0));
47
48 var line2 = new THREE.Line(geometry2, material);
49 line2.geometry.verticesNeedUpdate = true;
50 geometry2.dynamic = true;
51
52 var geometry3 = new THREE.Geometry();
53 geometry3.vertices.push(new THREE.Vector3(-26, 23, 0));
54 geometry3.vertices.push(new THREE.Vector3(-30, 22, 0));
55
56 var line3 = new THREE.Line(geometry3, material);
57 line3.geometry.verticesNeedUpdate = true;
58 geometry3.dynamic = true;
59
60 var geometry4 = new THREE.Geometry();
61 geometry4.vertices.push(new THREE.Vector3(-30, 24, 0));
62 geometry4.vertices.push(new THREE.Vector3(-26, 23, 0));
63
64 var line4 = new THREE.Line(geometry4, material);
65 line4.geometry.verticesNeedUpdate = true;
66 geometry4.dynamic = true;
67
68 var geometry5 = new THREE.Geometry();
69 geometry5.vertices.push(new THREE.Vector3(-26, 25, 0));
70 geometry5.vertices.push(new THREE.Vector3(-30, 24, 0));
71
72 var line5 = new THREE.Line(geometry5, material);
73 line5.geometry.verticesNeedUpdate = true;
74 geometry5.dynamic = true;
75
76 var geometry6 = new THREE.Geometry();
77 geometry6.vertices.push(new THREE.Vector3(-30, 26, 0));
78 geometry6.vertices.push(new THREE.Vector3(-26, 25, 0));
79
80 var line6 = new THREE.Line(geometry6, material);
81 line6.geometry.verticesNeedUpdate = true;
82 geometry6.dynamic = true;
83
84 var geometry7 = new THREE.Geometry();
85 geometry7.vertices.push(new THREE.Vector3(-26, 27, 0));
86 geometry7.vertices.push(new THREE.Vector3(-30, 26, 0));
87
88 var line7 = new THREE.Line(geometry7, material);
89 line7.geometry.verticesNeedUpdate = true;
90 geometry7.dynamic = true;
91
92 var geometry8 = new THREE.Geometry();
93 geometry8.vertices.push(new THREE.Vector3(-28, 28, 0));
94 geometry8.vertices.push(new THREE.Vector3(-26, 27, 0));
95
96 var line8 = new THREE.Line(geometry8, material);
97 line8.geometry.verticesNeedUpdate = true;
98 geometry8.dynamic = true;
99
100 var geometry9 = new THREE.Geometry();
101 geometry9.vertices.push(new THREE.Vector3(-30, 28, 0));
102 geometry9.vertices.push(new THREE.Vector3(-26, 28, 0));
103
104 var line9 = new THREE.Line(geometry9, material);
105
106 var geometry10 = new THREE.Geometry();
107 geometry10.vertices.push(new THREE.Vector3(-30, 28, 0));
108 geometry10.vertices.push(new THREE.Vector3(-29, 30, 0));
109
110 var line10 = new THREE.Line(geometry10, material);
111
112 var geometry11 = new THREE.Geometry();
113 geometry11.vertices.push(new THREE.Vector3(-29, 28, 0));
114 geometry11.vertices.push(new THREE.Vector3(-28, 30, 0));
115
116 var line11 = new THREE.Line(geometry11, material);
117
118 var geometry12 = new THREE.Geometry();
119 geometry12.vertices.push(new THREE.Vector3(-28, 28, 0));
120 geometry12.vertices.push(new THREE.Vector3(-27, 30, 0));
121
122 var line12 = new THREE.Line(geometry12, material);
123
124 var geometry13 = new THREE.Geometry();
125 geometry13.vertices.push(new THREE.Vector3(-27, 28, 0));
126 geometry13.vertices.push(new THREE.Vector3(-26, 30, 0));
127
128 var line13 = new THREE.Line(geometry13, material);
129
130 var geometry14 = new THREE.Geometry();
131 geometry14.vertices.push(new THREE.Vector3(-40, 20.25, 0));
132 geometry14.vertices.push(new THREE.Vector3(-42, 21, 0));
133
134 var line14 = new THREE.Line(geometry14, material);
135
136 var geometry15 = new THREE.Geometry();
137 geometry15.vertices.push(new THREE.Vector3(-40, 19.75, 0));
138 geometry15.vertices.push(new THREE.Vector3(-42, 19, 0));
139
140 var line15 = new THREE.Line(geometry15, material);
141
142 var geometry16 = new THREE.Geometry();
143 geometry16.vertices.push(new THREE.Vector3(-42, 19, 0));
144 geometry16.vertices.push(new THREE.Vector3(-42, 21, 0));
145
146 var line16 = new THREE.Line(geometry16, material);
147
148 var geometry17 = new THREE.Geometry();
149 geometry17.vertices.push(new THREE.Vector3(-42, 21, 0));
150 geometry17.vertices.push(new THREE.Vector3(-43, 22, 0));
151
152 var line17 = new THREE.Line(geometry17, material);
153
154 var geometry18 = new THREE.Geometry();
155 geometry18.vertices.push(new THREE.Vector3(-42, 20, 0));
156 geometry18.vertices.push(new THREE.Vector3(-43, 21, 0));
157
158 var line18 = new THREE.Line(geometry18, material);
159
160 var geometry19 = new THREE.Geometry();
161 geometry19.vertices.push(new THREE.Vector3(-42, 19, 0));
162 geometry19.vertices.push(new THREE.Vector3(-43, 20, 0));
163
164 var line19 = new THREE.Line(geometry19, material);
165
166 scene.add(line);
167 scene.add(line1);
168 scene.add(line2);
169 scene.add(line3);
170 scene.add(line4);
171 scene.add(line5);
172 scene.add(line6);
173 scene.add(line7);
174 scene.add(line8);
175 scene.add(line9);
176 scene.add(line10);
177 scene.add(line11);
178 scene.add(line12);
179 scene.add(line13);
180 scene.add(line14);
181 scene.add(line15);
182 scene.add(line16);
183 scene.add(line17);
184 scene.add(line18);
185 scene.add(line19);
186 scene.add(circle);
187 scene.add(circle1);
188 rr.render(scene, camera);
189
190 var controls = new function()
191 {
192 this.jestkost = 0.8;
193 this.mass = 0.2;
194 this.g = 0.5;
195 this.a = 4;
196 this.l = 16;
197 }
198
199 var gui = new dat.GUI();
200 gui.add(controls, 'jestkost', 0.8, Math.PI);
201 gui.add(controls, 'mass', 0.001, 0.24);
202 gui.add(controls, 'g', 0.1, 0.98);
203
204 window.addEventListener('resize', onWindowResize, false);
205
206 renderer();
207
208 function onWindowResize()
209 {
210 camera.aspect = window.innerWidth/window.innerHeight;
211 camera.updateProjectionMatrix();
212 rr.setSize(window.innerWidth, window.innerHeight);
213 renderer();
214 }
215
216 function renderer()
217 {
218 step+=0.1;
219
220 var koef = controls.mass*controls.g*controls.l*controls.l/(controls.jestkost*controls.a*controls.a);
221 var arg = Math.sqrt(controls.jestkost*controls.a*controls.a/(controls.mass*controls.l*controls.l));
222 var koef1 = (line.geometry.vertices[1].y-20)*(line.geometry.vertices[1].y-20);
223 var koef2 = controls.a/controls.l;
224
225 line.geometry.vertices[1].y=-koef*Math.cos(arg*step)-koef+20;
226 line.geometry.vertices[1].x=Math.sqrt(controls.l*controls.l-koef1);
227 line.geometry.verticesNeedUpdate = true;
228 line1.geometry.vertices[1].y=(-koef*Math.cos(arg*step)-koef+110)*koef2;;
229 line1.geometry.verticesNeedUpdate = true;
230 line2.geometry.vertices[1].y=(-koef*Math.cos(arg*step)-koef+80)*koef2;
231 line2.geometry.vertices[0].y=(-koef*Math.cos(arg*step)-koef+86)*koef2;
232 line2.geometry.verticesNeedUpdate = true;
233 line3.geometry.vertices[1].y=(-koef*Math.cos(arg*step)-koef+86)*koef2;
234 line3.geometry.vertices[0].y=(-koef*Math.cos(arg*step)-koef+90)*koef2;
235 line3.geometry.verticesNeedUpdate = true;
236 line4.geometry.vertices[1].y=(-koef*Math.cos(arg*step)-koef+90)*koef2;
237 line4.geometry.vertices[0].y=(-koef*Math.cos(arg*step)-koef+94)*koef2;
238 line4.geometry.verticesNeedUpdate = true;
239 line5.geometry.vertices[1].y=(-koef*Math.cos(arg*step)-koef+94)*koef2;
240 line5.geometry.vertices[0].y=(-koef*Math.cos(arg*step)-koef+98)*koef2;
241 line5.geometry.verticesNeedUpdate = true;
242 line6.geometry.vertices[1].y=(-koef*Math.cos(arg*step)-koef+98)*koef2;
243 line6.geometry.vertices[0].y=(-koef*Math.cos(arg*step)-koef+102)*koef2;
244 line6.geometry.verticesNeedUpdate = true;
245 line7.geometry.vertices[1].y=(-koef*Math.cos(arg*step)-koef+102)*koef2;
246 line7.geometry.vertices[0].y=(-koef*Math.cos(arg*step)-koef+106)*koef2;
247 line7.geometry.verticesNeedUpdate = true;
248 line8.geometry.vertices[1].y=(-koef*Math.cos(arg*step)-koef+106)*koef2;
249 line8.geometry.vertices[0].y=(-koef*Math.cos(arg*step)-koef+110)*koef2;
250 line8.geometry.verticesNeedUpdate = true;
251 circle.position.x=Math.sqrt(controls.l*controls.l-koef1);
252 circle.position.y=-koef*Math.cos(arg*step)-koef+20;;
253 circle1.position.x=-40;
254 circle1.position.y=20;
255 requestAnimationFrame(renderer);
256 rr.render(scene, camera);
257
258 document.getElementById("td1").innerHTML = line.geometry.vertices[1].x;
259 document.getElementById("td2").innerHTML = line.geometry.vertices[1].y;
260 }
261 }
Используемые библиотеки
- gui.js
- jquery.min.js
- orbit_controls.js
- script.js
- stats.js
- three.min.js
Возможности программы
- изменение жесткости пружины
- изменение ускорения свободного падения
Решение частного случая
Условия задачи: Стержень длины , на конце которой помещен груз массы , может поворачиваться вокруг оси . На расстоянии от оси к стержню прикреплена пружина с коэффициентом жесткости . Определить собственную частоту колебаний груза, если стержень в положении равновесия занимает горизонтальное положение. Массой стержня пренебречь.
Решение: - изменение координаты пружины по y; - изменение координаты грузика по y;
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