{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Mode d'emploi\n", "\n", "Executez les cellules DANS l'ORDRE, les unes après les autres. \n", "\n", "Si les graphiques n'apparaissent pas, ce qui arrive si vous avez recliqué sur le lien go.epfl.ch/oscillateurs, fermez le fichier en fermant l'onglet et rouvrez le depuis le menu à gauche. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Oscilateur harmonique libre et amorti (ou non)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nous considérons l'oscilateur harmonique libre et amorti.\n", "\n", "Une masse $m$ est accrochée à un ressort de constante de raideur $k$ et écartée de sa position d'équilibre de $x_0$, puis lâchée avec une vitesse initiale $v_0$.\n", "\n", "La masse est plongée dans un fluide et le coefficient de frottement visqueux laminaire est $b_l= K\\eta$\n", "\n", "$$\\Omega_0=\\sqrt{k/m}$$\n", "\n", "$$T_0=2\\pi/\\Omega_0$$\n", "\n", "$$\\gamma=(b_l/2m)$$\n", "\n", "L'équation différentielle du mouvement est:\n", "\n", "$$\\ddot x (t) + 2 \\gamma \\dot x(t) +\\Omega_0^2 x(t) = 0$$\n", "\n", "l'équation caractéristique associée est\n", "\n", "$$\\lambda^2+2\\gamma \\lambda+\\Omega_0^2=0$$\n", "\n", "son déterminant réduit est $\\Delta '=(\\gamma^2-\\Omega_0^2)$\n", "\n", "Si $\\Delta ' \\neq 0$, les racines de l'équation sont:\n", "\n", "$$\\lambda_1=-\\gamma +(\\Delta ')^{0.5}$$\n", "\n", "$$\\lambda_2=-\\gamma -(\\Delta ')^{0.5}$$\n", "\n", "Les solutions de l'équadiff sont alors de la forme\n", "\n", "$$x_c(t)=C_1 e^{\\lambda_1 t}+C_2 e^{\\lambda_2 t}$$\n", "\n", "Les conditions initiales donnent \n", "$$C_1=\\frac{\\lambda_2 x_0 - v_0}{\\lambda_2-\\lambda_1}$$\n", "\n", "$$C_2=\\frac{\\lambda_1 x_0 - v_0}{\\lambda_1-\\lambda_2}$$\n", "\n", "Attention! $\\lambda_1$ et $\\lambda_2$, $C_1$ et $C_2$ sont complexes\n", "\n", "La solution physique est la partie réelle de $x_c$.\n", "\n", "Si $\\Delta ' = 0$, la solution est la partie réelle de:\n", "\n", "$$x_c(t)=[x_0+(v_0+\\gamma x_0)t ]e^{-\\gamma t}$$\n", "\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", "
\n", " \n", " Loading BokehJS ...\n", "
\n" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "'use strict';\n", "(function(root) {\n", " function now() {\n", " return new Date();\n", " }\n", "\n", " const force = true;\n", "\n", " if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n", " root._bokeh_onload_callbacks = [];\n", " root._bokeh_is_loading = undefined;\n", " }\n", "\n", "const JS_MIME_TYPE = 'application/javascript';\n", " const HTML_MIME_TYPE = 'text/html';\n", " const EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n", " const CLASS_NAME = 'output_bokeh rendered_html';\n", "\n", " /**\n", " * Render data to the DOM node\n", " */\n", " function render(props, node) {\n", " const script = document.createElement(\"script\");\n", " node.appendChild(script);\n", " }\n", "\n", " /**\n", " * Handle when an output is cleared or removed\n", " */\n", " function handleClearOutput(event, handle) {\n", " function drop(id) {\n", " const view = Bokeh.index.get_by_id(id)\n", " if (view != null) {\n", " view.model.document.clear()\n", " Bokeh.index.delete(view)\n", " }\n", " }\n", "\n", " const cell = handle.cell;\n", "\n", " const id = cell.output_area._bokeh_element_id;\n", " const server_id = cell.output_area._bokeh_server_id;\n", "\n", " // Clean up Bokeh references\n", " if (id != null) {\n", " drop(id)\n", " }\n", "\n", " if (server_id !== undefined) {\n", " // Clean up Bokeh references\n", " const cmd_clean = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n", " cell.notebook.kernel.execute(cmd_clean, {\n", " iopub: {\n", " output: function(msg) {\n", " const id = msg.content.text.trim()\n", " drop(id)\n", " }\n", " }\n", " });\n", " // Destroy server and session\n", " const cmd_destroy = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n", " cell.notebook.kernel.execute(cmd_destroy);\n", " }\n", " }\n", "\n", " /**\n", " * Handle when a new output is added\n", " */\n", " function handleAddOutput(event, handle) {\n", " const output_area = handle.output_area;\n", " const output = handle.output;\n", "\n", " // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n", " if ((output.output_type != \"display_data\") || (!Object.prototype.hasOwnProperty.call(output.data, EXEC_MIME_TYPE))) {\n", " return\n", " }\n", "\n", " const toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n", "\n", " if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n", " toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n", " // store reference to embed id on output_area\n", " output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n", " }\n", " if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n", " const bk_div = document.createElement(\"div\");\n", " bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n", " const script_attrs = bk_div.children[0].attributes;\n", " for (let i = 0; i < script_attrs.length; i++) {\n", " toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n", " toinsert[toinsert.length - 1].firstChild.textContent = bk_div.children[0].textContent\n", " }\n", " // store reference to server id on output_area\n", " output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n", " }\n", " }\n", "\n", " function register_renderer(events, OutputArea) {\n", "\n", " function append_mime(data, metadata, element) {\n", " // create a DOM node to render to\n", " const toinsert = this.create_output_subarea(\n", " metadata,\n", " CLASS_NAME,\n", " EXEC_MIME_TYPE\n", " );\n", " this.keyboard_manager.register_events(toinsert);\n", " // Render to node\n", " const props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n", " render(props, toinsert[toinsert.length - 1]);\n", " element.append(toinsert);\n", " return toinsert\n", " }\n", "\n", " /* Handle when an output is cleared or removed */\n", " events.on('clear_output.CodeCell', handleClearOutput);\n", " events.on('delete.Cell', handleClearOutput);\n", "\n", " /* Handle when a new output is added */\n", " events.on('output_added.OutputArea', handleAddOutput);\n", "\n", " /**\n", " * Register the mime type and append_mime function with output_area\n", " */\n", " OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n", " /* Is output safe? */\n", " safe: true,\n", " /* Index of renderer in `output_area.display_order` */\n", " index: 0\n", " });\n", " }\n", "\n", " // register the mime type if in Jupyter Notebook environment and previously unregistered\n", " if (root.Jupyter !== undefined) {\n", " const events = require('base/js/events');\n", " const OutputArea = require('notebook/js/outputarea').OutputArea;\n", "\n", " if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n", " register_renderer(events, OutputArea);\n", " }\n", " }\n", " if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n", " root._bokeh_timeout = Date.now() + 5000;\n", " root._bokeh_failed_load = false;\n", " }\n", "\n", " const NB_LOAD_WARNING = {'data': {'text/html':\n", " \"
\\n\"+\n", " \"

\\n\"+\n", " \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n", " \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n", " \"

\\n\"+\n", " \"\\n\"+\n", " \"\\n\"+\n", " \"from bokeh.resources import INLINE\\n\"+\n", " \"output_notebook(resources=INLINE)\\n\"+\n", " \"\\n\"+\n", " \"
\"}};\n", "\n", " function display_loaded(error = null) {\n", " const el = document.getElementById(\"a5ae12c2-0209-4ce8-aeb1-3727fa291ebe\");\n", " if (el != null) {\n", " const html = (() => {\n", " if (typeof root.Bokeh === \"undefined\") {\n", " if (error == null) {\n", " return \"BokehJS is loading ...\";\n", " } else {\n", " return \"BokehJS failed to load.\";\n", " }\n", " } else {\n", " const prefix = `BokehJS ${root.Bokeh.version}`;\n", " if (error == null) {\n", " return `${prefix} successfully loaded.`;\n", " } else {\n", " return `${prefix} encountered errors while loading and may not function as expected.`;\n", " }\n", " }\n", " })();\n", " el.innerHTML = html;\n", "\n", " if (error != null) {\n", " const wrapper = document.createElement(\"div\");\n", " wrapper.style.overflow = \"auto\";\n", " wrapper.style.height = \"5em\";\n", " wrapper.style.resize = \"vertical\";\n", " const content = document.createElement(\"div\");\n", " content.style.fontFamily = \"monospace\";\n", " content.style.whiteSpace = \"pre-wrap\";\n", " content.style.backgroundColor = \"rgb(255, 221, 221)\";\n", " content.textContent = error.stack ?? error.toString();\n", " wrapper.append(content);\n", " el.append(wrapper);\n", " }\n", " } else if (Date.now() < root._bokeh_timeout) {\n", " setTimeout(() => display_loaded(error), 100);\n", " }\n", " }\n", "\n", " function run_callbacks() {\n", " try {\n", " root._bokeh_onload_callbacks.forEach(function(callback) {\n", " if (callback != null)\n", " callback();\n", " });\n", " } finally {\n", " delete root._bokeh_onload_callbacks\n", " }\n", " console.debug(\"Bokeh: all callbacks have finished\");\n", " }\n", "\n", " function load_libs(css_urls, js_urls, callback) {\n", " if (css_urls == null) css_urls = [];\n", " if (js_urls == null) js_urls = [];\n", "\n", " root._bokeh_onload_callbacks.push(callback);\n", " if (root._bokeh_is_loading > 0) {\n", " console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n", " return null;\n", " }\n", " if (js_urls == null || js_urls.length === 0) {\n", " run_callbacks();\n", " return null;\n", " }\n", " console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n", " root._bokeh_is_loading = css_urls.length + js_urls.length;\n", "\n", " function on_load() {\n", " root._bokeh_is_loading--;\n", " if (root._bokeh_is_loading === 0) {\n", " console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n", " run_callbacks()\n", " }\n", " }\n", "\n", " function on_error(url) {\n", " console.error(\"failed to load \" + url);\n", " }\n", "\n", " for (let i = 0; i < css_urls.length; i++) {\n", " const url = css_urls[i];\n", " const element = document.createElement(\"link\");\n", " element.onload = on_load;\n", " element.onerror = on_error.bind(null, url);\n", " element.rel = \"stylesheet\";\n", " element.type = \"text/css\";\n", " element.href = url;\n", " console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n", " document.body.appendChild(element);\n", " }\n", "\n", " for (let i = 0; i < js_urls.length; i++) {\n", " const url = js_urls[i];\n", " const element = document.createElement('script');\n", " element.onload = on_load;\n", " element.onerror = on_error.bind(null, url);\n", " element.async = false;\n", " element.src = url;\n", " console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n", " document.head.appendChild(element);\n", " }\n", " };\n", "\n", " function inject_raw_css(css) {\n", " const element = document.createElement(\"style\");\n", " element.appendChild(document.createTextNode(css));\n", " document.body.appendChild(element);\n", " }\n", "\n", " const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-3.6.0.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-3.6.0.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-3.6.0.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-3.6.0.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-3.6.0.min.js\"];\n", " const css_urls = [];\n", "\n", " const inline_js = [ function(Bokeh) {\n", " Bokeh.set_log_level(\"info\");\n", " },\n", "function(Bokeh) {\n", " }\n", " ];\n", "\n", " function run_inline_js() {\n", " if (root.Bokeh !== undefined || force === true) {\n", " try {\n", " for (let i = 0; i < inline_js.length; i++) {\n", " inline_js[i].call(root, root.Bokeh);\n", " }\n", "\n", " } catch (error) {display_loaded(error);throw error;\n", " }if (force === true) {\n", " display_loaded();\n", " }} else if (Date.now() < root._bokeh_timeout) {\n", " setTimeout(run_inline_js, 100);\n", " } else if (!root._bokeh_failed_load) {\n", " console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n", " root._bokeh_failed_load = true;\n", " } else if (force !== true) {\n", " const cell = $(document.getElementById(\"a5ae12c2-0209-4ce8-aeb1-3727fa291ebe\")).parents('.cell').data().cell;\n", " cell.output_area.append_execute_result(NB_LOAD_WARNING)\n", " }\n", " }\n", "\n", " if (root._bokeh_is_loading === 0) {\n", " console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n", " run_inline_js();\n", " } else {\n", " load_libs(css_urls, js_urls, function() {\n", " console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n", " run_inline_js();\n", " });\n", " }\n", "}(window));" ], "application/vnd.bokehjs_load.v0+json": "'use strict';\n(function(root) {\n function now() {\n return new Date();\n }\n\n const force = true;\n\n if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n root._bokeh_onload_callbacks = [];\n root._bokeh_is_loading = undefined;\n }\n\n\n if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n root._bokeh_timeout = Date.now() + 5000;\n root._bokeh_failed_load = false;\n }\n\n const NB_LOAD_WARNING = {'data': {'text/html':\n \"
\\n\"+\n \"

\\n\"+\n \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n \"

\\n\"+\n \"\\n\"+\n \"\\n\"+\n \"from bokeh.resources import INLINE\\n\"+\n \"output_notebook(resources=INLINE)\\n\"+\n \"\\n\"+\n \"
\"}};\n\n function display_loaded(error = null) {\n const el = document.getElementById(\"a5ae12c2-0209-4ce8-aeb1-3727fa291ebe\");\n if (el != null) {\n const html = (() => {\n if (typeof root.Bokeh === \"undefined\") {\n if (error == null) {\n return \"BokehJS is loading ...\";\n } else {\n return \"BokehJS failed to load.\";\n }\n } else {\n const prefix = `BokehJS ${root.Bokeh.version}`;\n if (error == null) {\n return `${prefix} successfully loaded.`;\n } else {\n return `${prefix} encountered errors while loading and may not function as expected.`;\n }\n }\n })();\n el.innerHTML = html;\n\n if (error != null) {\n const wrapper = document.createElement(\"div\");\n wrapper.style.overflow = \"auto\";\n wrapper.style.height = \"5em\";\n wrapper.style.resize = \"vertical\";\n const content = document.createElement(\"div\");\n content.style.fontFamily = \"monospace\";\n content.style.whiteSpace = \"pre-wrap\";\n content.style.backgroundColor = \"rgb(255, 221, 221)\";\n content.textContent = error.stack ?? error.toString();\n wrapper.append(content);\n el.append(wrapper);\n }\n } else if (Date.now() < root._bokeh_timeout) {\n setTimeout(() => display_loaded(error), 100);\n }\n }\n\n function run_callbacks() {\n try {\n root._bokeh_onload_callbacks.forEach(function(callback) {\n if (callback != null)\n callback();\n });\n } finally {\n delete root._bokeh_onload_callbacks\n }\n console.debug(\"Bokeh: all callbacks have finished\");\n }\n\n function load_libs(css_urls, js_urls, callback) {\n if (css_urls == null) css_urls = [];\n if (js_urls == null) js_urls = [];\n\n root._bokeh_onload_callbacks.push(callback);\n if (root._bokeh_is_loading > 0) {\n console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n return null;\n }\n if (js_urls == null || js_urls.length === 0) {\n run_callbacks();\n return null;\n }\n console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n function on_load() {\n root._bokeh_is_loading--;\n if (root._bokeh_is_loading === 0) {\n console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n run_callbacks()\n }\n }\n\n function on_error(url) {\n console.error(\"failed to load \" + url);\n }\n\n for (let i = 0; i < css_urls.length; i++) {\n const url = css_urls[i];\n const element = document.createElement(\"link\");\n element.onload = on_load;\n element.onerror = on_error.bind(null, url);\n element.rel = \"stylesheet\";\n element.type = \"text/css\";\n element.href = url;\n console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n document.body.appendChild(element);\n }\n\n for (let i = 0; i < js_urls.length; i++) {\n const url = js_urls[i];\n const element = document.createElement('script');\n element.onload = on_load;\n element.onerror = on_error.bind(null, url);\n element.async = false;\n element.src = url;\n console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n document.head.appendChild(element);\n }\n };\n\n function inject_raw_css(css) {\n const element = document.createElement(\"style\");\n element.appendChild(document.createTextNode(css));\n document.body.appendChild(element);\n }\n\n const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-3.6.0.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-3.6.0.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-3.6.0.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-3.6.0.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-3.6.0.min.js\"];\n const css_urls = [];\n\n const inline_js = [ function(Bokeh) {\n Bokeh.set_log_level(\"info\");\n },\nfunction(Bokeh) {\n }\n ];\n\n function run_inline_js() {\n if (root.Bokeh !== undefined || force === true) {\n try {\n for (let i = 0; i < inline_js.length; i++) {\n inline_js[i].call(root, root.Bokeh);\n }\n\n } catch (error) {display_loaded(error);throw error;\n }if (force === true) {\n display_loaded();\n }} else if (Date.now() < root._bokeh_timeout) {\n setTimeout(run_inline_js, 100);\n } else if (!root._bokeh_failed_load) {\n console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n root._bokeh_failed_load = true;\n } else if (force !== true) {\n const cell = $(document.getElementById(\"a5ae12c2-0209-4ce8-aeb1-3727fa291ebe\")).parents('.cell').data().cell;\n cell.output_area.append_execute_result(NB_LOAD_WARNING)\n }\n }\n\n if (root._bokeh_is_loading === 0) {\n console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n run_inline_js();\n } else {\n load_libs(css_urls, js_urls, function() {\n console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n run_inline_js();\n });\n }\n}(window));" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from cmath import *\n", "\n", "from bokeh.layouts import row, column\n", "from bokeh.models import CustomJS, Slider\n", "from bokeh.plotting import figure, show, ColumnDataSource\n", "\n", "from bokeh.io import push_notebook, show, output_notebook\n", "from ipywidgets import interact\n", "#from bokeh.resources import INLINE \n", "\n", "output_notebook()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Définition des fonctions importantes" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def omega0(k,m):\n", " oz=np.sqrt(k/m)\n", " return oz\n", "\n", "def gamma(bl,m):\n", " ga=bl/(2*m)\n", " return ga\n", "\n", "def fac_qual(k,m,bl):\n", " fq = np.sqrt(k*m)/bl\n", " return fq\n", "\n", "def deltaprime(k,m,bl):\n", " dp=gamma(bl,m)**2-omega0(k,m)**2+0j\n", " return dp\n", "\n", "def osciamo(k,m,bl,xzero,vzero,t):\n", " if (deltaprime(k,m,bl)!=0):\n", " gamma1=-gamma(bl,m)+deltaprime(k,m,bl)**(1/2)\n", " gamma2=-gamma(bl,m)-deltaprime(k,m,bl)**(1/2)\n", " C1=(gamma2*xzero-vzero)/(gamma2-gamma1)\n", " C2=(gamma1*xzero-vzero)/(gamma1-gamma2)\n", " solc=C1*np.exp(gamma1*t)+C2*np.exp(gamma2*t)\n", " sol=solc.real\n", " else:\n", " sol=(xzero+(vzero+gamma(bl,m)*xzero)*t)*np.exp(-gamma(bl,m)*t)\n", " return sol \n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Définition de la figure" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "p = figure(width=800, height=400)\n", "\n", "#valeurs initiales\n", "k=50\n", "m=5\n", "bl=0\n", "xzero=1\n", "vzero=0\n", "\n", "t = np.linspace(0,40,1000)\n", "x1 = osciamo(k,m,bl,xzero,vzero,t)\n", "expga = np.exp(-gamma(bl,m)*t)\n", "\n", "pos = p.line(t,x1,line_width=3,legend_label=\"position\")\n", "ga = p.line(t,expga,color=\"orange\",line_width=2,legend_label=\"exp(-gamma*t)\")\n", "\n", "p.legend.location = \"top_right\"\n", "p.legend.click_policy=\"hide\"\n", "\n", "\n", "def update(m=5, k = 50, bl = 0): #, xzero= 1 , vzero = 0):\n", " pos.data_source.data['y'] = osciamo(k,m,bl,xzero,vzero,t)\n", " ga.data_source.data['y'] = np.exp(-gamma(bl,m)*t)\n", " push_notebook()\n", " print('Omega_0 = {:0.2f}[rad/s]'.format(omega0(k,m)),\", gamma = \", gamma(bl,m)) \n", " dp = deltaprime(k,m,bl)**0.5\n", " dpr = dp.real\n", " dpi = dp.imag\n", " print('-')\n", " print('Partie réelle de racine de delta prime {:0.2f}[rad/s]'.format(dpr))\n", " print('-')\n", " print('Partie imaginaire de racine de delta prime {:0.2f}[rad/s]'.format(dpi))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Let's Play!\n", "\n", "Cette figure montre l'évolution de $x(t)$. On trace aussi l'enveloppe exponentielle $e^{-\\gamma t}$\n", "\n", "Qu'observe-t-on léorsqu'on fait varier les trois paramètres $m$, $k$ et $b_l$ ?\n", "\n", "Regardez comment varie $\\Omega_0$ par rapport à $\\gamma$, et ce que vallent les parties réeeles et imaginaires du déterminant réduit $\\Delta'$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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\"},\"shape\":[1000],\"dtype\":\"float64\",\"order\":\"little\"}],[\"y\",{\"type\":\"ndarray\",\"array\":{\"type\":\"bytes\",\"data\":\"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" const render_items = [{\"docid\":\"70763dbb-271a-4f9b-bc8a-0af6877a293f\",\"roots\":{\"p1001\":\"b8cf6aaa-5711-4f3d-96aa-97057a593e26\"},\"root_ids\":[\"p1001\"],\"notebook_comms_target\":\"p1056\"}];\n", " void root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n", " }\n", " if (root.Bokeh !== undefined) {\n", " embed_document(root);\n", " } else {\n", " let attempts = 0;\n", " const timer = setInterval(function(root) {\n", " if (root.Bokeh !== undefined) {\n", " clearInterval(timer);\n", " embed_document(root);\n", " } else {\n", " attempts++;\n", " if (attempts > 100) {\n", " clearInterval(timer);\n", " console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n", " }\n", " }\n", " }, 10, root)\n", " }\n", "})(window);" ], "application/vnd.bokehjs_exec.v0+json": "" }, "metadata": { "application/vnd.bokehjs_exec.v0+json": { "id": "p1001" } }, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Widget Javascript not detected. It may not be installed or enabled properly. Reconnecting the current kernel may help.\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "596b315a80164931a9bfb955b73bf6eb" } }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(p, notebook_handle=True)\n", "interact(update, m = (1,10,1), k = (1,50,1), bl = (0,200,1));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Oscilateur forcé. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On conserve les mêmes notations, mais cette fois on soumet l'oscilateur à une force $F_0 \\cos (\\omega_e t)$\n", "\n", "Comme la force d'excitation est obtenue par le déplacement sinusoidal d'une membrane, avec un déplacement d'amplitude $x_{e,0}$, qui provoque sur le ressort une force d'amplitude $F_0=k x_{e,0}$, le déplacement de l'excitation est égal à\n", "\n", "$$\\frac{F_0}{k}\\cos(\\omega_e t)$$\n", "\n", "L'équadiff devient \n", "\n", "$$\\ddot x (t) + 2 \\gamma \\dot x(t) +\\Omega_0^2 x(t) = (F_0/m) \\cos (\\omega_e t)$$\n", "\n", "En notation complexe et avec $f=F_0/m$\n", "\n", "$$\\ddot x (t) + 2 \\gamma \\dot x(t) +\\Omega_0^2 x(t) = f e^{i\\omega_e t}$$\n", "\n", "La solution en régime permanent est $x_{1,c}(t)= \\chi_0 e^{i\\omega_e t}$ avec $\\chi_0=A e^{i \\varphi}$. $A(\\omega_e)$ est l'amplitude et $\\varphi(\\omega_e)$ le déphasage.\n", "\n", "$$\\chi_0 = \\frac{f}{-(\\omega_e^2-\\Omega_0^2)+i(2\\gamma\\omega_e)}$$\n", "\n", "La solution générale est la somme du régime permanent plus la solution générale de l'équation différentielle sans second membre trouvée au paragraphe précédent ($x_{2,c}(t)$).\n", "\n", "Les constantes d'intégration $C_1$ et $C_2$ se déterminent sur $x_{c}(t)=x_{1,c}(t)+x_{2,c}(t)$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Définition des fonctions" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "#amplitude de l'excitation\n", "def exci(omegae,k,f,t):\n", " ex=(f/k*m)*np.cos(omegae*t)\n", " return ex\n", "\n", "def chizero(omegae,k,m,bl,f):\n", " chizero=f/complex((omega0(k,m)**2-omegae**2),(2*gamma(bl,m)*omegae))\n", " return chizero\n", "\n", "#Fonctions pour calculer les amplitudes et déphasages pour une série de pulsation d'escitation\n", "# L'amplitude est divisée par f*m/m afin de la normaliser à l'amplitude d'excitation\n", "def amplitudes(k,m,bl,f,omegae_v):\n", " amp=[]\n", " for i in omegae_v:\n", " amp.append(abs(chizero(i,k,m,bl,f))*(k/(f*m)))\n", " return amp\n", "\n", "def dephasages(k,m,bl,f,omegae_v):\n", " deph=[]\n", " for i in omegae_v:\n", " deph.append(phase(chizero(i,k,m,bl,f)))\n", " return deph\n", "\n", "#x1(t) complexe\n", "def regpermc(omegae,k,m,bl,f,t):\n", " rp=chizero(omegae,k,m,bl,f)*complex(np.cos(omegae*t),np.sin(omegae*t))\n", " return rp\n", "\n", "#x2(t) complexe, avec C1 et C2 déterminés grace à x0 et v0\n", "def xdeuxdetc(omegae,k,m,bl,f,xzero,vzero,t):\n", " if (deltaprime(k,m,bl)!=0):\n", " gamma1=-gamma(bl,m)+deltaprime(k,m,bl)**(1/2)\n", " gamma2=-gamma(bl,m)-deltaprime(k,m,bl)**(1/2)\n", " C1=(gamma2*xzero-vzero-gamma2*chizero(omegae,k,m,bl,f)+(0+1j)*chizero(omegae,k,m,bl,f)*omegae)/(gamma2-gamma1)\n", " C2=(gamma1*xzero-vzero-gamma1*chizero(omegae,k,m,bl,f)+(0+1j)*chizero(omegae,k,m,bl,f)*omegae)/(gamma1-gamma2)\n", " sol=C1*np.exp(gamma1*t)+C2*np.exp(gamma2*t)\n", " else:\n", " A=xzero-chizero(omegae,k,m,bl,f)\n", " B=vzero+gamma(bl,m)*xzero-gamma(bl,m)*chizero(omegae,k,m,bl,f)-(0+1j)*chizero(omegae,k,m,bl,f)*omegae\n", " sol=(A+B*t)*np.exp(-gamma(bl,m)*t)\n", " return sol \n", " \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Tracé de la figure" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "p2 = figure(width=950, height=400,y_range=(-1, 1))\n", "\n", "# valeurs initiales (pour l'oscilateur dans l'air, l'eau et l'huile)\n", "# tableau (k,m,bl,f,xzero,vzero)\n", "\n", "air = (15,0.19,0.02,1,0,0)\n", "fluide1 = (15,0.19,0.05,1,0,0)\n", "eau = (15,0.19,0.3,1,0,0)\n", "huile = (15,0.19,1.5,1,0,0)\n", "\n", "choix = eau\n", "k = choix[0]\n", "m = choix[1]\n", "bl = choix[2]\n", "f = choix[3]\n", "xzero = choix[4]\n", "vzero = choix[5]\n", "omegae = 7.1 #Pulsation d'excitation\n", "tmin = 0\n", "tmax = 1000\n", "\n", "t2 = np.linspace(0,50,1000)\n", "omegae_v1 = np.linspace(5,15,2000)\n", "\n", "def permreal(omegae,k,m,bl,f,t):\n", " pr=[]\n", " for i in t:\n", " pr.append(regpermc(omegae,k,m,bl,f,i).real)\n", " pr=np.array(pr)\n", " return pr\n", "\n", "def x2real(omegae,k,m,bl,f,xzero,vzero,t):\n", " x2r=[]\n", " for i in t:\n", " x2r.append(xdeuxdetc(omegae,k,m,bl,f,xzero,vzero,i).real)\n", " x2r=np.array(x2r)\n", " return x2r\n", "\n", "\n", "excitation = p2.line(t2,exci(omegae,k,f,t2),line_width=3 ,alpha=0.7, legend_label=\"excitation\")\n", "amorti = p2.line(t2,x2real(omegae,k,m,bl,f,xzero,vzero,t2),color=\"green\",alpha=0.7,line_width=3,legend_label=\"x2 : solution générale de l'équation SSM\")\n", "total = p2.line(t2,permreal(omegae,k,m,bl,f,t2)+x2real(omegae,k,m,bl,f,xzero,vzero,t2),color=\"red\",alpha=0.7,line_width=3,legend_label=\"solution totale\")\n", "permanent = p2.line(t2,permreal(omegae,k,m,bl,f,t2),color=\"black\",line_width=1,legend_label=\"x1 : régime permanent\")\n", "\n", "p2.legend.location = \"top_right\"\n", "p2.legend.click_policy=\"hide\"\n", "p2.xaxis.axis_label=\"temps[s]\"\n", "\n", "dp = figure(width=400, height=300)\n", "deph=dp.line(omegae_v1,dephasages(k,m,bl,f,omegae_v1),line_width=3)\n", "\n", "dp.xaxis.axis_label=\"omega excitation[rad/s]\"\n", "dp.yaxis.axis_label=\"déphasage[rad]\"\n", "\n", "\n", "deph_vx=np.array([omegae])\n", "deph_vy=np.array([phase(chizero(omegae,k,m,bl,f))])\n", "deph_v=dp.scatter(deph_vx,deph_vy,color=\"red\",size=8)\n", "\n", "ap = figure(width=400, height=300)\n", "amp=ap.line(omegae_v1,amplitudes(k,m,bl,f,omegae_v1),line_width=3)\n", "\n", "ap.xaxis.axis_label=\"omega excitation[rad/s]\"\n", "ap.yaxis.axis_label=\"Amplitude relative\"\n", "\n", "\n", "amp_vx = np.array([omegae])\n", "amp_vy = np.array([abs(chizero(omegae,k,m,bl,f))*(k/(f*m))])\n", "amp_v = ap.scatter(amp_vx,amp_vy,color=\"red\",size=8)\n", "\n", "def update2(milieu, omegae=8.3): #, xzero= 1 , vzero = 0):\n", " if milieu==\"eau\": choix = eau\n", " if milieu==\"air\": choix=air\n", " if milieu==\"huile\": choix=huile\n", " if milieu==\"fluide1\": choix=fluide1\n", " k = choix[0]\n", " m = choix[1]\n", " bl = choix[2]\n", " f = choix[3]\n", " xzero = choix[4]\n", " vzero = choix[5]\n", " excitation.data_source.data['y'] = exci(omegae,k,f,t2)\n", " permanent.data_source.data['y'] = permreal(omegae,k,m,bl,f,t2)\n", " amorti.data_source.data['y'] = x2real(omegae,k,m,bl,f,xzero,vzero,t2)\n", " total.data_source.data['y'] = permreal(omegae,k,m,bl,f,t2)+x2real(omegae,k,m,bl,f,xzero,vzero,t2)\n", " deph.data_source.data['y'] = dephasages(k,m,bl,f,omegae_v1)\n", " amp.data_source.data['y'] = amplitudes(k,m,bl,f,omegae_v1)\n", " deph_v.data_source.data['x'] = np.array([omegae])\n", " deph_v.data_source.data['y'] = np.array([phase(chizero(omegae,k,m,bl,f))])\n", " amp_v.data_source.data['x'] = np.array([omegae])\n", " amp_v.data_source.data['y'] = np.array([abs(chizero(omegae,k,m,bl,f))*k/(f*m)])\n", "\n", " push_notebook()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Let's play !\n", "\n", "On peut choisir quatre milieux différents: air, eau, une \"huile\" très épaisse et un fluide intermédiare entre l'eau et l'huile.\n", "L'eau et l'air correspondent à la manip des auditoires. \n", "\n", "On trace la courbe de la position en fonction du temps pour quatre contributions.\n", "\n", "1- l'excitation, du moteur qui force le déplacement du ressort. \n", "\n", "2- la solution du régime permanent (qui est la solution particulière de l'équation différentielle)\n", "\n", "3- La solution générale de l'équation sans second membre (solution de l'oscillateur amorti non forcé)\n", "\n", "4- La solution totale, qui montre le régime transitoire et l'établissement des oscillations\n", "\n", "On peut varier la valeur de la pulsation d'excitation. Les boutons à droite de la figure permettent de zoomer et déplacer.\n", "\n", "Les deux courbes dessous montrent le déphasage et l'amplitude relative (amplitude divisée par amplitude d'esxitation)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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\"},\"shape\":[1000],\"dtype\":\"float64\",\"order\":\"little\"}],[\"y\",{\"type\":\"ndarray\",\"array\":{\"type\":\"bytes\",\"data\":\"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root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n", " }\n", " if (root.Bokeh !== undefined) {\n", " embed_document(root);\n", " } else {\n", " let attempts = 0;\n", " const timer = setInterval(function(root) {\n", " if (root.Bokeh !== undefined) {\n", " clearInterval(timer);\n", " embed_document(root);\n", " } else {\n", " attempts++;\n", " if (attempts > 100) {\n", " clearInterval(timer);\n", " console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n", " }\n", " }\n", " }, 10, root)\n", " }\n", "})(window);" ], "application/vnd.bokehjs_exec.v0+json": "" }, "metadata": { "application/vnd.bokehjs_exec.v0+json": { "id": "p1245" } }, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Widget Javascript not detected. It may not be installed or enabled properly. Reconnecting the current kernel may help.\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "2020e451761140ae8a04ab321d459482" } }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(column(p2,row(dp,ap)), notebook_handle=True)\n", "interact(update2, omegae = (5,15,.1),milieu=[\"eau\",\"air\",\"huile\",\"fluide1\"]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Tracé des courbes de déphasage et amplitude\n", "\n", "Ici on peut faire varier la masse, la constante de raideur du ressort et le coefficient de frottement, et regarder comment se comportent les courbes du déphasage et de l'amplitude relative" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "#Fonction qui retourne omega resonnance si il existe et -1 sinon\n", "def omegares(k,m,bl):\n", " orsq=(omega0(k,m))**2-2*(gamma(bl,m))**2\n", " if orsq > 0 : omegares = np.sqrt(orsq)\n", " else : omegares= -1\n", " return omegares \n", "\n", "# Fonction qui retourne l'amplitude à omegares si elle existe\n", "def ampres(k,m,bl,f):\n", " ores=omegares(k,m,bl)\n", " if ores >=0 : ampres = abs(chizero(ores,k,m,bl,f))*(k/(f*m))\n", " else : ampres = -1\n", " return ampres\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "dp2 = figure(width=450, height=350)\n", "ap2 = figure(width=450, height=350)\n", "\n", "\n", "# valeurs initiales\n", "k=10\n", "m=.1\n", "bl=1\n", "f=1\n", "\n", "\n", "omegae_v2 = np.linspace(0.01,20,2000)\n", "\n", "deph2 = dp2.line(omegae_v2,dephasages(k,m,bl,f,omegae_v2),line_width=3)\n", "\n", "amp2 = ap2.line(omegae_v2,amplitudes(k,m,bl,f,omegae_v2),line_width=3)\n", "\n", "resonnancex=np.array([omegares(k,m,bl),omegares(k,m,bl)])\n", "resonnancey=np.array([0,ampres(k,m,bl,f)])\n", "\n", "dp2.xaxis.axis_label=\"pulsation d'excitation[rad/s]\"\n", "dp2.yaxis.axis_label=\"déphasage[rad]\"\n", "ap2.xaxis.axis_label=\"pulsation d'excitation[rad/s]\"\n", "ap2.yaxis.axis_label=\"amplitude relative\"\n", "\n", "ores = ap2.line(resonnancex,resonnancey, color='black')\n", "\n", "def update3(k=10, m=.1,bl=1): # f=1\n", " deph2.data_source.data['y'] = dephasages(k,m,bl,f,omegae_v2)\n", " amp2.data_source.data['y'] = amplitudes(k,m,bl,f,omegae_v2)\n", " if (omegares(k,m,bl) > 0 and bl>0):\n", " ores.data_source.data['x'] = np.array([omegares(k,m,bl),omegares(k,m,bl)])\n", " ores.data_source.data['y'] = np.array([0,ampres(k,m,bl,f)])\n", " else :\n", " ores.data_source.data['x'] = np.array([0,0]) \n", " ores.data_source.data['y'] = np.array([0,0])\n", " \n", " if omegares(k,m,bl) >=0 : \n", " print(' omega_resonnance = {:0.2f}[rad/s]'.format(omegares(k,m,bl)))\n", " else : print(\"Pas de résonnance\") \n", " if bl > 0 : print('facteur de qualité, Q = {:0.2f}'.format(fac_qual(k,m,bl)))\n", " else : print('le facteur de qualité Q est infini') \n", " push_notebook()\n", " \n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Let's play !\n", "\n", "Observez la qualité de la résonnance en fonction des paramètres" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n", " }\n", " if (root.Bokeh !== undefined) {\n", " embed_document(root);\n", " } else {\n", " let attempts = 0;\n", " const timer = setInterval(function(root) {\n", " if (root.Bokeh !== undefined) {\n", " clearInterval(timer);\n", " embed_document(root);\n", " } else {\n", " attempts++;\n", " if (attempts > 100) {\n", " clearInterval(timer);\n", " console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n", " }\n", " }\n", " }, 10, root)\n", " }\n", "})(window);" ], "application/vnd.bokehjs_exec.v0+json": "" }, "metadata": { "application/vnd.bokehjs_exec.v0+json": { "id": "p1365" } }, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Widget Javascript not detected. It may not be installed or enabled properly. Reconnecting the current kernel may help.\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "e587cd686cd0478aa42b2e39822e1623" } }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(row(dp2,ap2), notebook_handle=True)\n", "interact(update3,k=(1,50,1),m=(.1,1,.1),bl=(0,10,.1));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Amplitude en fonction de la pulsation réduite\n", "\n", "Tracé universel de l'amplitude relative en fonction de la pulsation réduite $\\omega_e/\\Omega_0=X$ et du facteur de qualité $Q$:\n", "\n", "$$A(\\omega_e)/A(0)=\\frac{Q}{\\sqrt{Q^2(X^2-1)^2+X^2}}$$\n", "\n", "La résonnance se produit pour $X_\\text{res}=\\sqrt{1-Q^2/2}$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "def AmpQual(Q,X):\n", " aq = Q/np.sqrt(Q**2*(X**2-1)**2+X**2)\n", " return aq\n", "\n", "ap3 = figure(width=700, height=350)\n", "\n", "# valeur initiale\n", "Qual=1\n", "\n", "Xtab = np.linspace(0.01,3,500)\n", "\n", "amp3 = ap3.line(Xtab,AmpQual(Qual,Xtab),line_width=3)\n", "\n", "ap3.xaxis.axis_label=\"pulsation réduite\"\n", "ap3.yaxis.axis_label=\"Amplitude relative\"\n", "\n", "def update4(Qual=1): #\n", " amp3.data_source.data['y'] = AmpQual(Qual,Xtab)\n", " Xressquared=1-1/(2*Qual**2)\n", " if Xressquared >= 0 : print('X_resonnance = {:0.3f}'.format(np.sqrt(Xressquared)))\n", " else : print('Pas de résonnance')\n", " push_notebook()\n", " \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Let's play\n", "\n", "Le seul facteur qu'on peut faire varier est le facteur de qualité. \n", "\n", "Regardez ou se situe la résonnance par rapport à $X=1$" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
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It may not be installed or enabled properly. Reconnecting the current kernel may help.\n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "0034a4454d3b4e91975fe31cdb7bd512" } }, "metadata": {}, "output_type": "display_data" } ], "source": [ "show(ap3, notebook_handle=True)\n", "interact(update4,Qual=(0.1,50,0.1));" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Remarque, pour des raisons pratiques, on s'arrête à un facteur de qualité de 50. 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