{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Déphasage de la réponse d'un oscillateur"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cette petite animation permet de visualiser d'une foction de transfert complexe pour un oscillateur harmonique, et comment sela se traduit par un déphasage visualisé sur la composante réeele."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.animation import FuncAnimation\n",
    "from IPython.display import Image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gen():\n",
    "    for ot in np.linspace(0,6*np.pi,100):\n",
    "        yield f*np.cos(ot), f*np.sin(ot), A*np.cos(ot+phi), A*np.sin(ot+phi), ot\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def init():\n",
    "    axes[0].set_ylim(-2, 2)\n",
    "    axes[0].set_xlim(-2, 2)\n",
    "    axes[0].set_xlabel('x')\n",
    "    axes[0].set_ylabel('y')\n",
    "    axes[0].set_aspect('equal')\n",
    "    axes[0].grid()\n",
    "    \n",
    "    axes[1].set_ylim(-2, 2)\n",
    "    axes[1].set_xlim(0, 6*np.pi)\n",
    "    axes[1].set_xlabel('temps')\n",
    "    axes[1].grid()\n",
    "        \n",
    "    axes[1].legend()\n",
    "#    axes[2].legend()\n",
    "    return \n",
    "\n",
    "def func(data):\n",
    "    fx, fy, Ax, Ay, ot = data\n",
    "#    time_text.set_text(r'$\\theta$ = %.2f $\\pi$' % (Rt/np.pi))\n",
    "    fx_.append(fx)\n",
    "    Ax_.append(Ax)\n",
    "    ang.append(ot)\n",
    "#    ptFx, ptFy = np.array([fx,fy])\n",
    "#    ptAx, ptAy = np.array([Ax,Ay])\n",
    "    \n",
    "    exitation.set_data(ang, fx_)\n",
    "    response.set_data(ang,Ax_)\n",
    "    linef.set_data((0,fx), (0,fy)) #(xdebut , xfin), (ydebut,xfin)\n",
    "    lineA.set_data((0,Ax), (0,Ay)) #(xdebut , xfin), (ydebut,xfin)\n",
    "    projf.set_data((0,fx), (0.03,0.03)) #(xdebut , xfin), (ydebut,xfin)\n",
    "    projA.set_data((0,Ax), (-0.03,-0.03)) #(xdebut , xfin), (ydebut,xfin)\n",
    "    pointf.set_data(fx, fy)\n",
    "    pointA.set_data(Ax, Ay)\n",
    "    return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x73d41e99cf70>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 936x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1,2,figsize=(13,5))\n",
    "#time_text = axes[0].text(0.05, 0.8, '', transform=axes[0].transAxes)\n",
    "\n",
    "#Plot layout setup\n",
    "f = 1.2\n",
    "A = 1.7\n",
    "phi = np.pi/6\n",
    "linef, = axes[0].plot([], [], 'r-', lw=2)\n",
    "lineA, = axes[0].plot([], [], 'b-', lw=2)\n",
    "projf, = axes[0].plot([], [], 'r-', lw=3)\n",
    "projA, = axes[0].plot([], [], 'b-', lw=3)\n",
    "\n",
    "#circle_line, = axes[0].plot([], [], 'g', lw=3)\n",
    "pointf, = axes[0].plot([], [], 'ro', ms=5)\n",
    "pointA, = axes[0].plot([], [], 'bo', ms=5)\n",
    "\n",
    "exitation, = axes[1].plot([], [], 'r-', lw=3, label='Excitation')\n",
    "response, = axes[1].plot([], [], 'b-', lw=3, label='Réponse')\n",
    "\n",
    "circle1 = plt.Circle((0, 0), 1, color='r',fill=False)\n",
    "axes[0].add_artist(circle1)\n",
    "\n",
    "\n",
    "fx_, fy_ = [], []\n",
    "Ax_, Ay_ = [], []\n",
    "ang = []\n",
    "    \n",
    "plt.ioff()\n",
    "\n",
    "plt.rcParams['animation.html'] = 'html5'\n",
    "\n",
    "animation = FuncAnimation(fig, func, gen, init_func=init, blit=False, interval=1./18*2500)\n",
    "animation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "hide_input": false,
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
