{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercice - Collé-glissé\n",
    "Mise en équation de l'exercice vu en cours.\n",
    "On commence par définir les grandeurs modélisant le problème."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "m=0.1\n",
    "k=0.1\n",
    "g=9.8\n",
    "f=0.6\n",
    "xo=2\n",
    "v=1\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On calcule ensuite des grandeurs caractéristiques permettant de choisir la durée de la modélisation et les conditions initiales.\n",
    "On choisit de partir d'un instant où le glissment commence :\n",
    "$$v(0)=v $$\n",
    "$$x(0)=x_o+\\frac{fmg}{k}$$\n",
    "On calcule la période propre du signal pour définir la durée de l'expérience."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "wo=np.sqrt(k/m)\n",
    "To=2*np.pi/wo\n",
    "\n",
    "xmax=xo+f*m*g/k"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On crée ensuite les listes t, x(t) et vx(t)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "N=500\n",
    "t=np.linspace(0,3*To,N)\n",
    "x=np.zeros(N)\n",
    "vx=np.zeros(N)\n",
    "dt=t[1]-t[0]\n",
    "\n",
    "x[0]=xo\n",
    "vx[0]=v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On remplit ensuite les listes vx et x de proche en proche en distinguant les cas glissement et non glissement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "glissement = False\n",
    "epsilon=0.05\n",
    "\n",
    "for i in range (1,N):\n",
    "    if glissement :\n",
    "        vx[i]=(f*g-k*(x[i-1]-xo)/m)*dt+vx[i-1]\n",
    "        x[i]=vx[i]*dt+x[i-1]\n",
    "        glissement=((vx[i]-v)<epsilon)\n",
    "    else :\n",
    "        vx[i]=v\n",
    "        x[i]=x[i-1]+v*dt\n",
    "        glissement=((k*(x[i-1]-xo)-f*m*g)>epsilon)\n",
    "    \n",
    "\n",
    "      "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On affiche ensuite les courbes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x224533c07f0>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PSDQ7imE6tvPjtot6sXxfPntyS82OY5fy6lqeW5FOUs+OXDaou9lxDDO2XzjDenbk1TWZLjPr4dHSKt5cd4BLBnRz+s1dKdQeKCWvjE+3HuamkTHEhrc3O46hbruwF6FBvrywKt3sKHb553eZFJ00f7V3oymleHByP/LLqvl482Gz49jlueXp2LQ25eauFGoPo7XmycX7CAn05b4J1lwdxJGCA3y58+JY1qYXkpxVbHacszp8vJJ3N2Rx1dAoBkaFmh3HcKNiwxgV25nX12ZSWVNndpyz2pVTwsIdR7jtwl706BTk9P1LofYwK/bls+lgMQ9M6kdIkGsOR26tm0fGENben+dWWHuqzWeWp+LtpZg91RqrvTvDg5P7UXSyhvc3Wncu8Z/GGoS19+dug2bHa4kUag9SXWtj3tJU4iKCud7iq4M4UqCfN/eMi2XzIetOYL/lUDFL9+Rz58WxRHTwnOneh/XsxNi4cN5af8Cyc4kv2XOU5OwTPDS5n2lzrUih9iDv/pBFTnEVj89ItPzqII52/QXRdA8J4LmV1jurrq/X/G1JCt1CApg5xjkDKKzkwUlxlFh0LvHqWhtPL00joVsHrknqYVoOz/rf6sEKyqv557f7mZjgOquDOJK/jzf3T+zHrpwSFu+21vDlhTuOsDu3lD9NiXPLdryWDIgKYcbAbixYf4D8UmvNevivDYc4UlLF4zMS8DZxrhUp1B7i+RXp1NjqeewS11kdxNGuGhZFQrcOPLMszTItYRWn6pi/PI1BPUK5YrDzBlBYzcNT46mvh+dWWKc7p6Csmte/y2RyYgSjYs09uZFC7QH2Hinlv9tyuXV0L3q52OogjuTtpZg7I5EjJVW8vf6g2XEAeGPtAQrKT/EXN5gd71z06BTErRfGsHBHLnuPWKPn/fmVDSc3j1pg6TMp1G7up9VBOgX5cc9411sdxNFGxnZm6nldeX2t+W+zc09UsuD7g1w+uDtDozuamsUKZo3rQ8cgP/62JMX0+wg7c0r+d3JjhaXPpFC7uSV7jrI16wQPTYmjg4uuDuJoj05PwFavmb8izdQcTy9Lw0s1vO0X0CHAlz9O6semg8WsTDlmWo76es1fvt5LWHt/7rXIyY0Uajd2+h3ra028Y2010Z2D+N2FvVi4/QhbDpkzCOaHzCKWNM6O192NZsc7V9ef34N+Ee15clGKaYNgPt+Wy67cUh6ZFm+Zpc+kULuxt9cf5EhJFXNnJJp6x9qK7h3fh8jQQB5ZuJtTdc69sVhda+PRL/cQ0zmIu0waQGFVPt5ezLtyAEdKqnhl9X6n77+0qpZnl6cxrGdHp86O1xIp1G4qv7Sa19ceYOp5XRkZ29nsOJbTzt+HeVf250BhBa9959xVy19evZ/s45X8/VcDCPD1vHa8lpwf04lfJ/Xg/zYcIvVomVP3PW9JCiVVtTxx2XmWmmtFCrWbmr8iDVu9tsQda6saG9eFywd35421mWQcc86c1fvySnn7+4NcmxRlesuXlc2ZFk9IoC+PfrkHm5PWV1yXUchnybnMHNOb/pEhTtmnvaRQu6GdOSUs3H6E2y7qRXRn508g40rmzkikvb8Pf/x0p+GXQKprbTzw6S46BvnJL9AWdGznx18uTWTH4RLeXGf8O57y6loe+WI3fbq0t+RkZS0WaqVUnFJq52kfZUqp+50RTrSe1ponF+0jPNifWeOsccfayjq392f+1YPYl1fGs8uMHWzxzLI00o+V8/w1AwkNco/1KY102aDuzBjYjZdWZbA7t8TQfc1bkkp+WTXzrx5oyctR9qxCnq61Hqy1HgwMAyqBLw1PJtrkm115bD9cwp+mxNHe3znrubm6SYkR3DIqhnd+OMS3aca0ha1OOcZ7G7O4ZVSM266o42hKKeZdMYAuwf7c/8lOw7pAvt55hE+25nDHxbGW7Wdv7aWPCcABrbV15yT0YJU1dTyzLI0BkSFcPTTK7DguZc60eBK6deDBz3Zx+HilQ587s+Ak93+6k/6RHdxqRXFnCAny5YVrB3PoeAVzvtjj8IEwBwpP8ujCPST17MiDk/o59LkdqbWF+jrgP009oJSaqZRKVkolFxYWnnsy0WpvrWtYz22uhw9HbosAX29e/+1QNHDre1sorXLMlJsllTXM/CAZfx8v3roxyZJvq61uZGxnHpocxze78nhzneOG/hdX1HDbe1vx9/Xm1d8MsfSMknYnU0r5AZcB/23qca31Aq11ktY6KTw83FH5hJ3ySqp4a/0BZgx0/npu7qJXWDvevGEYh4sruePDZKpqzu3m4slTddzy7lZyT1Txxg3DiJSBLW1299hYZgzsxvwVaSzalXfOz1dda2PmB8nklVbz9k3D6BZi7Z9Na36FTAO2a63NG9spmvXMsjS0Rt5an6MRvTvz/DWD2HKomN+9t7XN10XLq2v5/ftb2XOklH/+ZgjDe8kvz3OhlOK5qwdxfs9O3P/pTlbsy2/zc1XV2Lj9g2SSs0/wwjWDGNbT+j+b1hTq62nmsocw17bsYr7ZlcfMMb2J6ijteOfq8sGRvHjtYDYfOs51CzaRV1LVqu/PK6nimjd/JDnrBC9eO4jJ53U1KKlnCfTz5p1bz2dAZAj3fLydz7bmtPo5Sqtq+d17W9mQWcT8qwZyqYus9G5XoVZKBQGTgIXGxhGtVV+veWJRChEd/LnzYhmO7ChXDInkrRuTOFhYwaWvbmDFvvwWb2RprflmVx4zXt3AkRNVvHfrcC734DmmjdDe34cPbhvOiN6dmf3Fbp5YtM/uucX3HillxqvfszWrmJeuHcy157vO/Dd2FWqtdaXWurPW2hoTxYr/+bJxdZCHp8bTTtrxHGpSYgRfzRpNeLA/d3y4jZve2cLGzCLqzxgpZ6vXbNhfxE3vbOEP/9lBj05BfDlrtEeupOMMHQJ8efeW87llVAzv/pDF5JfWsyrl2C9+Lj8pOnmKvy9N5YrXfqDOpvn0jpFcYaF5POyhjJj3NSkpSScnJzv8ecXPVZyqY9zza+kWGsiXd42STg+D1Nrq+WhTNq+s2U9JZS0dg3w5r3sIIUG+lFbWsi+vlBOVtYS19+OusX24eWRPS3cQuJONmUX8+au9HCyqoGfnIMbHdyEuIphAP2+OlVWzNesE6zIKqamr59qkKOZMS6BTO2sONlJKbdNaJzX5mBRq1/X8inT++V0mC+8eZdlGfXdSXWtjxb58vt9fRGbBScqqawn296FfRDBj47owIaGLtN+ZoNZWz5LdR1m44wibDh6npq7+f49FhgYyKTGCG0b0pE+X9iambJkUajeUU1zJhBfXMb1/V16+bojZcYSwhDpbPUdLq6mx1dO5nZ9LDdU/W6GWi5ou6pllaXgrxcPSjifE//h4e9Gjk/t1PsmFNBe0+eBxluw5yp0Xx1q+UV8Ice6kULsYW73mycUpdA8JYOaY3mbHEUI4gRRqF/P5thz25ZXx8LR4Av3kxpUQnkAKtQspr67luRXpDOvZkctcZESVEOLcSaF2If/8LpOikzXMnZFoqfXchBDGkkLtIrKPV/DuhiyuGhrFoB6hZscRQjiRFGoX8felqfh4K2ZPjTM7ihDCyaRQu4CNB4pYse8Ys8b1IaJDgNlxhBBOJoXa4mz1micXpRDVMZDbLuxldhwhhAmkUFvcJ1sPk5ZfzqPTE2QeCSE8lBRqCyutquWFlRkM79WJaf1l8nkhPJUUagt7dc1+TlRKO54Qnk4KtUUdLDzJexuzuHZYD/pHhpgdRwhhIinUFjVvSSoBvt48NEXa8YTwdFKoLWh9RiFr0gq4Z3wfwoP9zY4jhDCZvYvbhiqlPldKpSmlUpVSI40O5qnqbPU8tTiFnp2DuHV0jNlxhBAWYO/CAa8Ay7XWVyul/AD3m5nbIj7ecpj9BSd568Zh+PtIO54Qwo5CrZTqAIwBbgHQWtcANcbG8kwllTW8uCqDUbGdmZwYYXYcIYRF2HPpozdQCLyrlNqhlPo/pVS7MzdSSs1USiUrpZILCwsdHtQTvLx6P2VVtcy9VNrxhBD/nz2F2gcYCryhtR4CVABzztxIa71Aa52ktU4KDw93cEz3l1lQzoebsrl+eDTxXTuYHUcIYSH2FOpcIFdrvbnx75/TULiFAz21OJUgP28emNTP7ChCCItpsVBrrfOBHKXUTw29E4AUQ1N5mO/SCliXUch9E/rSub204wkhfs7ero97gX83dnwcBG41LpJnqbXV89SSFHqHteOmkTFmxxFCWJBdhVprvRNIMjiLR/rgx2wOFlbwr5uT8POR8UdCiF+SymCi4ooaXlmdwUV9wxgf38XsOEIIi5JCbaKXVmVQUWOT2fGEEGclhdok6fnl/HtzNjdcEE3fiGCz4wghLEwKtQm01jy1OIXgAF/unyjteEKIs5NCbYLVqQVsyCzijxP70rGdn9lxhBAWJ4XayU7V2Zi3JIU+Xdrz2xE9zY4jhHABUqid7P2NWWQdr+TxGYn4esvhF0K0TCqFExWdPMWrazIZFxfOxf1kPhQhhH2kUDvRCyvTqaq18ecZiWZHEUK4ECnUTrIvr5RPtuZw08gYYsPbmx1HCOFCpFA7gdaaJxelEBroy30T+podRwjhYqRQO8GKfflsPlTMA5PjCAnyNTuOEMLFSKE2WHWtjXlLU4mLCOb683uYHUcI4YKkUBvsnR8OkVNcxdxLE/GRdjwhRBtI5TBQQVk1r32byaTECEb3CTM7jhDCRUmhNtBzK9KpsdXz2PQEs6MIIVyYFGqD7Mkt5fPtufxudC9iwn6xaLsQQthNCrUBtNY8sWgfnYL8mDW+j9lxhBAuTgq1ARbvPkpy9gkemhJHhwBpxxNCnBu71kxUSmUB5YANqNNay/qJzaiutfHMsjQSunXg2iRpxxNCnDt7VyEHGKe1LjIsiZtYsP4gR0qqeOHaQXh7yfJaQohzJ5c+HCi/tJo31h5gWv+ujOjd2ew4Qgg3YW+h1sBKpdQ2pdTMpjZQSs1USiUrpZILCwsdl9CFzF+ehk1rHpV2PCGEA9lbqEdrrYcC04BZSqkxZ26gtV6gtU7SWieFh3veXMs7Dp9g4Y4j/P7CXvToFGR2HCGEG7GrUGut8xr/LAC+BIYbGcrVaK15cnEK4cH+3D1O2vGEEI7VYqFWSrVTSgX/9DkwGdhrdDBX8vXOPHYcLmH2lDja+7fm/qwQQrTMnqoSAXyplPpp+4+11ssNTeVCKmvqeGZZGgMiQ7hqaJTZcYQQbqjFQq21PggMckIWl/TmuoPkl1Xz6m+G4CXteEIIA0h73jk4UlLFW+sOMGNgN86P6WR2HCGEm5JCfQ6eWZYGwCPSjieEMJAU6jZKzipm0a487hjTm8jQQLPjCCHcmBTqNqivb2jH69ohgDvHxpodRwjh5qRQt8HCHUfYnVvKw9PiCPKTdjwhhLGkULdSxak65i9PY3CPUC4fFGl2HCGEB5BC3Uqvr82koPwUf7k0UdrxhBBOIYW6FXKKK3n7+0NcOSSSIdEdzY4jhPAQUqhb4ellqXgrxeypcWZHEUJ4ECnUdtp08DhL9+Rz58WxdAuRdjwhhPNIobaDrV7z5KIUuocEMHNMb7PjCCE8jBRqO/w3OYeUo2XMmZ5AoJ+32XGEEB5GCnULyqtreX5lOkk9O3LpwG5mxxFCeCAp1C3453eZFJ2sYe6liTRO9SqEEE4lhfosso9X8O6GLK4eFsXAqFCz4wghPJQU6rOYtyQVX2/F7CnSjieEMI8U6mZszCxiZcox7h7Xhy4dAsyOI4TwYFKom1Bnq+fJxSlEdQzktgt7mR1HCOHhpFA34ZOtOaTll/Po9AQCfKUdTwhhLrsLtVLKWym1Qym12MhAZiutquXFVRkM79WJaf27mh1HCCFadUZ9H5BqVBCr+Mea/ZyorGHuDGnHE0JYg12FWikVBVwC/J+xccx1oPAk72/M4tdJPegfGWJ2HCGEAOw/o34ZmA3UG5jFdH9fkkqArzcPTpZ2PCGEdbRYqJVSM4ACrfW2FrabqZRKVkolFxYWOiygs6zPKGRNWgH3ju9DeLC/2XGEEOJ/7DmjHg1cppTKAj4BxiulPjpzI631Aq11ktY6KTw83MExjVVnq+epxSn07BzELaNjzJzh30IAAArpSURBVI4jhBA/02Kh1lo/orWO0lrHANcB32qtbzA8mRP9e/Nh9hec5LHpCfj7SDueEMJaPL6PuqSyhpdWZzC6T2cmJUaYHUcIIX7BpzUba63XAmsNSWKSl1fvp6yqlselHU8IYVEefUa9/1g5H27K5vrh0cR37WB2HCGEaJLHFmqtNU8tSSXIz5sHJvUzO44QQjTLYwv1d+kFrM8o5L4JfencXtrxhBDW5ZGFuqaunr8tTqV3WDtuGhljdhwhhDgrjyzUH27K5mBRBX+ekYCfj0ceAiGEC/G4KlVcUcMrqzMY0y+ccXFdzI4jhBAt8rhC/eKqdCpqbDx+SYK04wkhXIJHFeq0/DI+3nyYG0f0pG9EsNlxhBDCLh5TqLXWPLU4hQ6Bvtw/sa/ZcYQQwm4eU6hXpRzjh8zj/HFiP0KD/MyOI4QQdvOIQn2qzsa8pan06dKe31wQbXYcIYRoFY8o1O/9kEX28Uoen5GIr7dH/JOFEG7E7atWYfkpXv02k/HxXbi4n2vNky2EEOABhfqFlelU19p47JIEs6MIIUSbuHWh3pdXyqfJOdw8KobY8PZmxxFCiDZx20KttebJRSl0DPLjDxOkHU8I4brctlAv35vP5kPFPDCpHyGBvmbHEUKINnPLQl1d29COF981mOvO72F2HCGEOCduWaj/teEQuSeqmDsjER9pxxNCuDi3q2IFZdW89l0mkxIjGNUnzOw4Qghxzlos1EqpAKXUFqXULqXUPqXUE84I1lbzV6RTa6vnsenSjieEcA/2rEJ+ChivtT6plPIFNiillmmtNxmcrdV255bw+bZc7hjTm5iwdmbHEUIIh2ixUGutNXCy8a++jR/ayFBt8VM7Xlh7P+4Z38fsOEII4TB2XaNWSnkrpXYCBcAqrfXmJraZqZRKVkolFxYWOjpnixbtPkpy9gkemhxHcIC04wkh3IddhVprbdNaDwaigOFKqf5NbLNAa52ktU4KD3funBrVtTaeWZpKYrcOXJMk7XhCCPfSqq4PrXUJsBaYakiaNlqw/iB5pdX85dJEvL1keS0hhHuxp+sjXCkV2vh5IDARSDM6mL3yS6t5Y+0Bpg/oygW9O5sdRwghHM6ero9uwPtKKW8aCvtnWuvFxsay37PL07BpzSPTpB1PCOGe7On62A0McUKWVtt++ARf7jjCrHGx9OgUZHYcIYQwhMuOTKyvb2jHCw/2566x0o4nhHBfLluov951hJ05JcyeEkd7f3uu4AghhGtyyUJdWVPHs8vSGRgVwlVDo8yOI4QQhnLJQv3m2gPkl1Uzd0YiXtKOJ4Rwcy5XqHNPVPLW+oNcOqg7STGdzI4jhBCGc7lC/ezydJSCOdPizY4ihBBO4VKFOjmrmEW78pg5JpbI0ECz4wghhFO4TKGur9c8sSiFrh0CuPPi3mbHEUIIp3GZQv3F9lz2HCllzrR4gvykHU8I4TlcolCfPFXH/BXpDIkO5fLB3c2OI4QQTuUShfr17zIpLD/F3BmJKCXteEIIz2L5Qp1TXMn/bTjElUMiGRLd0ew4QgjhdJYv1H9fmoq3Ujw8VdrxhBCeydKFetPB4yzbm89dY2PpGhJgdhwhhDCFZQu1rbEdLzI0kJljpB1PCOG5LFuo/5ucQ+rRMuZMiyfA19vsOEIIYRpLFury6lqeX5nO+TEdmTGwm9lxhBDCVJYs1P/8NpPjFTXMnXGetOMJITye5Qp1VlEF7/xwiKuHRjEgKsTsOEIIYTp7ViHvoZT6TimVqpTap5S6z8hA85am4uftxZ+mxBm5GyGEcBn2nFHXAQ9qrROAEcAspVSiEWF+yCxiVcox7h7Xhy4dpB1PCCHAjkKttT6qtd7e+Hk5kApEOjpIna2eJxel0KNTILdd2MvRTy+EEC6rVdPQKaVigCHA5iYemwnMBIiOjm51kOq6egb1CGF8fBdpxxNCiNMorbV9GyrVHlgHzNNaLzzbtklJSTo5OdkB8YQQwjMopbZprZOaesyurg+llC/wBfDvloq0EEIIx7Kn60MB/wJStdYvGh9JCCHE6ew5ox4N3AiMV0rtbPyYbnAuIYQQjVq8mai13gDI8EAhhDCJ5UYmCiGE+Dkp1EIIYXFSqIUQwuKkUAshhMXZPeClVU+qVCGQ3cZvDwOKHBjH0ayeD6yfUfKdO6tnlHyt11NrHd7UA4YU6nOhlEpubnSOFVg9H1g/o+Q7d1bPKPkcSy59CCGExUmhFkIIi7NioV5gdoAWWD0fWD+j5Dt3Vs8o+RzIcteohRBC/JwVz6iFEEKcRgq1EEJYnCmFWik1VSmVrpTKVErNaeJxpZT6R+Pju5VSQ52cr8UFfZVSY5VSpafNKDjXyRmzlFJ7Gvf9i1UaLHAM4047NjuVUmVKqfvP2Mapx1Ap9Y5SqkAptfe0r3VSSq1SSu1v/LNjM9971teswRmfU0qlNf4cv1RKhTbzvWd9TRiY769KqSMtza7pjGPYTL5PT8uWpZTa2cz3Gn782kxr7dQPwBs4APQG/IBdQOIZ20wHltEwa98IYLOTM3YDhjZ+HgxkNJFxLLDY2cfvtP1nAWFnedzUY9jEzzyfhoZ+044hMAYYCuw97WvzgTmNn88Bnm0m/1lfswZnnAz4NH7+bFMZ7XlNGJjvr8BDdrwGDD+GTeU74/EXgLlmHb+2fphxRj0cyNRaH9Ra1wCfAJefsc3lwAe6wSYgVCnVzVkBtZMW9DWYqcfwDBOAA1rrto5WdQit9Xqg+IwvXw683/j5+8AVTXyrPa9ZwzJqrVdqresa/7oJiDJi3/Zo5hjawynH8Gz5GhdBuRb4j6P3azQzCnUkkHPa33P5ZRG0ZxunONuCvsBIpdQupdQypdR5Tg0GGliplNrWuLDwmSxzDIHraP4/h5nHECBCa30UGn5BA12a2MZKx/J3NLxTakpLrwkj3dN4aeadZi4fWeEYXgQc01rvb+ZxM4/fWZlRqJtahODMHkF7tjGcaljQ9wvgfq112RkPb6fhrfwg4FXgKyfHG621HgpMA2Yppcac8bhVjqEfcBnw3yYeNvsY2ssqx/IxoA74dzObtPSaMMobQCwwGDhKw+WFM1nhGF7P2c+mzTp+LTKjUOcCPU77exSQ14ZtDKVaWNBXa12mtT7Z+PlSwFcpFeasfFrrvMY/C4AvaXhreTrTj2GjacB2rfWxMx8w+xg2OvbTJaHGPwua2Mb0Y6mUuhmYAfxWN15QPZMdrwlDaK2Paa1tWut64O1m9mvqMVRK+QC/Aj5tbhuzjp89zCjUW4G+SqlejWdb1wHfnLHNN8BNjZ0LI4DSn96eOkPjtayzLuirlOrauB1KqeE0HMvjTsrXTikV/NPnNNxs2nvGZqYew9M0exZj5jE8zTfAzY2f3wx83cQ29rxmDaOUmgo8DFymta5sZht7XhNG5Tv93seVzezX1GMITATStNa5TT1o5vGzixl3MGnoSMig4S7wY41fuxO4s/FzBbzW+PgeIMnJ+S6k4W3ZbmBn48f0MzLeA+yj4e71JmCUE/P1btzvrsYMljuGjRmCaCi8Iad9zbRjSMMvjKNALQ1neLcBnYE1wP7GPzs1btsdWHq216wTM2bScH33p9fim2dmbO414aR8Hza+xnbTUHy7mXUMm8rX+PX3fnrdnbat049fWz9kCLkQQlicjEwUQgiLk0IthBAWJ4VaCCEsTgq1EEJYnBRqIYSwOCnUQghhcVKohRDC4v4fy0EwuTslY+UAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(t,x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10d1790b8>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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U41DFvQByEjJqBRCwiy6g7Qgh5gF8bJPHpwE8I30/BuBELvthbK+66txIpQV8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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d213470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
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