DM5_resolution_numerique_dune_equation_differentielle.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# DM5 résolution numérique d'une équation différentielle"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Noms des étudiants :"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Éloi Drai - Jean-Raphaël Nottez - Aksil Mammar"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercice 1\n",
    "\n",
    "## 1)\n",
    "\n",
    "**a)** \n",
    "\n",
    "```\n",
    "  ————/——————|\n",
    " |           |—————\n",
    "(G)         (X)   (V)\n",
    " |           |—————\n",
    "  ————(A)————|\n",
    "```\n",
    "\n",
    "**b)** L'unité de $a$ est le $ VA^{-1} $ et celle de $b$ est le $ VA^{-3} $\n",
    "\n",
    "**c)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.optimize import curve_fit, root\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "i = [0, 0.018, 0.035, 0.051, 0.058, 0.066, 0.08, 0.089, 0.095, 0.103, 0.108, 0.115, 0.119, 0.124, 0.129]\n",
    "u = [0, 0.25, 0.88, 1.72, 2.16, 2.72, 3.76, 4.72, 5.28, 6.08, 6.64, 7.48, 7.88, 8.51, 9.2]\n",
    "\n",
    "def fu(i, a, b):\n",
    "    return a*i + b*i**3\n",
    "\n",
    "[a, b], _ = curve_fit(fu, i, u)\n",
    "\n",
    "u_fit = [fu(i, a, b) for i in np.linspace(0, .13, 1000)]\n",
    "\n",
    "plt.xlabel(\"i\")\n",
    "plt.ylabel(\"u(i)\")\n",
    "plt.plot(np.linspace(0, .13, 1000), u_fit, label=\"Modèle\")\n",
    "plt.scatter(i, u, label=\"Valeurs\", c=\"red\")\n",
    "plt.title(\"Caractéristique de la lampe (modèle/mesures)\")\n",
    "plt.legend()\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Relativement satisfaisant"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2)\n",
    "\n",
    "**a)**\n",
    "En régime permanent, le condensateur équivaut à un interrupteur ouvert.\n",
    "$i(\\infty) = 0$, $u_c(\\infty) = E$, $u(\\infty) = 0$\n",
    "\n",
    "**b)**\n",
    "Par continuité de la tension aux bornes d'un condensateur $ u_c(0^-) = u_c(0^+) = 0 $.\n",
    "\n",
    "Par la loi des mailles : $ u(0^+) = E $\n",
    "On résout $ ai^3 + bi = E \\iff ai^3 + bi - E = 0 $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.09415156362083682"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E = 5\n",
    "sol = root(lambda i: a*i + b*i**3 - E, 0)\n",
    "sol.x[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**c)**\n",
    "$ u = ai + bi^3 = E - \\frac{1}{C} \\times q(t) $\n",
    "\n",
    "En dérivant, on trouve.\n",
    "\n",
    "$ a\\frac{\\mathrm{d}i(t)}{\\mathrm{d}t} + b\\frac{\\mathrm{d}i(t)}{\\mathrm{d}t}3i(t)^2 = -\\frac{1}{C} \\times \\frac{\\mathrm{d}q(t)}{\\mathrm{d}t} \\iff \\frac{\\mathrm{d}i(t)}{\\mathrm{d}t}(a + 3bi(t)^2)  = -\\frac{i(t)}{C} $. \n",
    "\n",
    "Ce qui nous donne bien : $ \\frac{\\mathrm{d}i(t)}{\\mathrm{d}t}  = -\\frac{i(t)}{(a + 3bi(t)^2) \\cdot C} $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**d)**\n",
    "### Méthode d'Euler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "E = 5\n",
    "C = 1e-3\n",
    "Tf = 10*a*C\n",
    "N = 100\n",
    "i0 = 0.09415156362083682\n",
    "\n",
    "fp = lambda t, x: -x/((a + 3*b*x**2)*C)\n",
    "\n",
    "def euler(fp, x0, Tf, N):\n",
    "    t = np.linspace(0, Tf, N)\n",
    "    h = Tf / N\n",
    "    x = np.zeros(N)\n",
    "    x[0] = x0\n",
    "    for k in range(N-1):\n",
    "        x[k+1] = x[k] + h*fp(t[k], x[k])\n",
    "    return t, x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**e) f)**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig_eloi, (graphe_i, graphe_u) = plt.subplots(1, 2)\n",
    "fig_eloi.subplots_adjust(wspace=1)\n",
    "\n",
    "t, i, = euler(fp, i0, Tf, N)\n",
    "graphe_i.plot(t, i)\n",
    "graphe_i.set_xlabel(\"Temps (s)\")\n",
    "graphe_i.set_ylabel(\"Intensité (A)\")\n",
    "\n",
    "graphe_u.set_xlabel(\"Temps (s)\")\n",
    "graphe_u.set_ylabel(\"Tension (V)\")\n",
    "graphe_u.plot(t, a*i + b*i**3, c=\"red\")\n",
    "\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex II : Signal pseudo périodique"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1) Récupérer les données d'un tableau exel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# -*- coding: utf-8 -*-\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "T,I = [],[]\n",
    "\n",
    "try:\n",
    "    fic = open(\"RLC exp.TXT\")\n",
    "except IOError:\n",
    "    fic = open(\"RLC_exp.TXT\")\n",
    "for ligne in fic:\n",
    "    if ligne[0] != '#':\n",
    "        a,b= map(float,ligne.split())\n",
    "        T.append(a)\n",
    "        I.append(b)\n",
    "fic.close()\n",
    "\n",
    "plt.axis([1.1719E-6,0.00029883,-0.0025,0.0025])\n",
    "plt.scatter(T,I,label=\"Intensité (valeur expérimentales)\")\n",
    "plt.title(\"Graphique de l'intensité en fonction du temps\")\n",
    "plt.xlabel(\"Temps (s)\")\n",
    "plt.ylabel(\"Intensité (A)\")\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "plt.close()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On observe un signal pseudo périodique avec 10 oscillations, on peut estimer Q=10."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2) Utilisation d'un modèle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tau = 8.333291417290646e-05\n",
      "T1 = 2.8602476696603264e-05\n",
      "A = 2.4533315413629875e-08\n",
      "B = -0.002276127036846656\n"
     ]
    }
   ],
   "source": [
    "import scipy.optimize as so\n",
    "import numpy as np\n",
    "\n",
    "def f(t,tau,T,A,B):\n",
    "    return (A*np.cos(2*np.pi*t/T)+B*np.sin(2*np.pi*t/T))*np.exp(-t/tau)\n",
    "\n",
    "popt,pcov = so.curve_fit(f,T,I,bounds=([0.0,0.0,-0.005,-0.005],[0.0003,5*10**(-5),0.005,0.005]))\n",
    "tau = popt[0]\n",
    "print(\"tau =\",tau)\n",
    "T1 = popt[1]\n",
    "print(\"T1 =\",T1)\n",
    "A = popt[2]\n",
    "print(\"A =\",A)\n",
    "B = popt[3]\n",
    "print(\"B =\",B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Avec curve_fit on trouve : tau = 8.33329142e-05 s ; T = 2.86024767e-05 s; A = 2.45333154e-08 et B = -2.27612704e-03."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En effet vu qu'on a Q \"grand\" on peut exprimer : T = tau * delta avec delta = pi/Q ; Alors : Q = tau * pi / T."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Q = 9.152986076863826\n"
     ]
    }
   ],
   "source": [
    "Q = tau * np.pi / T1\n",
    "print(\"Q =\",Q)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ainsi Q vaut 9.152986076863828, sachant qu on avait estimer Q = 10, cette réponse est cohérente."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Donc on a T0 = tau * pi / Q."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T0 = 2.8602476696603264e-05\n"
     ]
    }
   ],
   "source": [
    "T0 = tau * np.pi / Q\n",
    "print(\"T0 =\",T0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "T0 vaut donc : 2.8602476696603264e-05 s."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3) Autre méthode pour trouver T et Tau"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tm = [2.1094e-05, 5.0391e-05, 7.8516e-05, 0.00010664, 0.00013594, 0.00016406, 0.00019336, 0.00022148, 0.00024961, 0.00027891]\n",
      "Im = [0.0017616, 0.0012399, 0.00088674, 0.0006272, 0.00044534, 0.00031658, 0.00022315, 0.00015943, 0.00011265, 8.0104e-05] \n",
      "Nombre de maximums = 10\n"
     ]
    }
   ],
   "source": [
    "def max_rel(T,I):\n",
    "    Im = []\n",
    "    Tm = []\n",
    "    croissant = 0\n",
    "    decroissant = 0\n",
    "    if T[0]<T[1] and I[0]<I[1]:\n",
    "        croissant = 1\n",
    "    else:\n",
    "        decroissant = 1\n",
    "    for i in range(len(T)-2):\n",
    "        if croissant == 1 and T[i]<T[i+1] and I[i]>I[i+1]:\n",
    "            Im.append(I[i])\n",
    "            Tm.append(T[i])\n",
    "            croissant,decroissant = 0,1\n",
    "        elif decroissant == 1 and T[i]<T[i+1] and I[i]<I[i+1]:\n",
    "            croissant,decroissant = 1,0\n",
    "    return Tm,Im\n",
    "\n",
    "Tm,Im = max_rel(T,I)\n",
    "print(\"Tm =\",Tm)\n",
    "print(\"Im =\",Im, \"\\nNombre de maximums =\",len(Tm))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour trouver T qu'on va nommer T2, on peut faire une moyenne des toutes les periodes calculer entre chaque maximums."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T2 = 2.5391e-05\n",
      "Ecart normalisé = 3.2114766966032626e-06\n"
     ]
    }
   ],
   "source": [
    "somme = 0\n",
    "for i in range(len(Tm)-1,1,-1):\n",
    "    somme += Tm[i]-Tm[i-1]\n",
    "T2 = somme/(len(Tm)-1)\n",
    "print(\"T2 =\", T2)\n",
    "print(\"Ecart normalisé =\",T1-T2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Avec cette méthode on trouve T = 2.5391e-05s, par rapport à la question 2a les résultats sont trés proche, l'écart normalisé vaut 3.2114766966032626e-06 ce qui est trés faible, cette méthode est plutot précise dans ce cas car nous avons un nombre d'oscillations important."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut donc calculer le décrément logarithmique :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Décrément logarithmique = 0.30906519755629136\n"
     ]
    }
   ],
   "source": [
    "delta = np.log(Im[0]/Im[-1])/len(Im)\n",
    "print(\"Décrément logarithmique =\",delta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comme delta = T/tau :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tau = 8.215418688600625e-05\n",
      "Ecart normalisé = 1.1787272869002134e-06\n"
     ]
    }
   ],
   "source": [
    "tau1 = T2/delta\n",
    "print(\"tau =\",tau1)\n",
    "print(\"Ecart normalisé =\",tau-tau1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "De même avec la methode du décrément logarithmique tau vaut 8.215418688600625e-05 et l'écart normalisé par rapport à la valeur du 2)a est 1.178727286900227e-06, on obtient 2 résultats qui sont donc trés proches. Ainsi nos résultats sont solide car ils se vérifient entre-eux par 2 méthodes différentes : curve_fit et par le décrément logaritgmique."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercice 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.\n",
    "En $t=0^{+}$ on a $U_{C}\\left(0^{+}\\right)=U_{C}\\left(0^{-}\\right)=1V$ et $i\\left(0^{+}\\right)=C\\cfrac{dU_{C}}{dt}\\left(0^{-}\\right)=0A$ par principe de continuité du condensateur."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.\n",
    "En régime permanent, c'est-à-dire en $t\\longrightarrow+\\infty$, $U_{C}\\left(+\\infty\\right)=0$ et $i\\left(+\\infty\\right)=C\\cfrac{dU_{C}}{dt}=0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.\n",
    "La loi des mailles nous donne l'équation suivante.\n",
    "\n",
    "$$U_{C}+U_{R}+U_{L}=0$$\n",
    "\n",
    "$$\\dfrac{q}{C}+Ri\\left(t\\right)+L\\dfrac{di}{dt}\\left(t\\right)=0$$\n",
    "\n",
    "$$\\dfrac{1}{C}i\\left(t\\right)+\\dfrac{R}{L}\\dfrac{di}{dt}\\left(t\\right)+L\\dfrac{d^{2}i}{dt^{2}}\\left(t\\right)=0$$\n",
    "\n",
    "$$\\dfrac{d^{2}i}{dt^{2}}\\left(t\\right)+\\dfrac{R}{L}\\dfrac{di}{dt}\\left(t\\right)+\\dfrac{1}{LC}i\\left(t\\right)=0$$\n",
    "\n",
    "Puis on considère $\\omega_{0}=\\cfrac{1}{\\sqrt{LC}},\\ Q=\\dfrac{1}{R}\\sqrt{\\dfrac{L}{C}}\\text{ et }\\lambda=\\dfrac{\\omega_{0}}{2Q}$:\n",
    "\n",
    "$$\\dfrac{d^{2}i}{dt^{2}}\\left(t\\right)+2\\lambda\\dfrac{di}{dt}\\left(t\\right)+\\omega^{2}_{0}i\\left(t\\right)=0\\ \\left(E\\right)$$\n",
    "\n",
    "On calcule $\\lambda$ et $\\omega_{0}$ à l'aide de $R=6000\\ \\Omega,\\ C=1\\times 10^{-7}F\\text{ et }L=0{,}0015H$:\n",
    "$\\omega_{0}=\\cfrac{1}{\\sqrt{LC}}\\approx 81\\ 649{,}65\\ rad\\cdot s^{-1},\\ Q\\approx 0{,}0204\\text{ et }\\lambda=\\dfrac{\\omega_{0}}{2Q}=\\dfrac{R}{2L}=2\\times 10^{6}\\ s^{-1}$\n",
    "\n",
    "Puis l'équation caractéristique de $\\left(E\\right)$ est la suivante:\n",
    "\n",
    "$$\\alpha^{2}+2\\lambda\\alpha+\\omega^{2}_{0}=0,\\ \\left(E_{c}\\right)$$\n",
    "\n",
    "Dont le discriminant est $\\Delta=4\\lambda^{2}-4\\omega^{2}_{0},\\ \\sqrt{\\Delta}=2\\sqrt{\\lambda^{2}-\\omega^{2}_{0}}$, on remarque ainsi que, puisque $\\lambda >\\omega_{0}$, la racine du discriminant est réelle.\n",
    "\n",
    "$$\\lambda >\\omega_{0}\\iff\\dfrac{\\omega_{0}}{2Q}>\\omega_{0}\\iff Q<\\dfrac{1}{2}$$\n",
    "\n",
    "Le régime est donc apériodique puisque $Q=0{,}0204$ satisfait la condition précédente."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.\n",
    "Les deux solutions $\\alpha_{1}$ et $\\alpha_{2}$ de $\\left(E_{c}\\right)$ s'expriment par:\n",
    "\n",
    "$$\\alpha_{1}=-\\lambda+\\sqrt{\\lambda^{2}-\\omega^{2}_{0}}\\text{ et }\\alpha_{2}=-\\lambda-\\sqrt{\\lambda^{2}-\\omega^{2}_{0}}$$\n",
    "\n",
    "Donc la solution générale de $\\left(E\\right)$ est:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "i\\left(t\\right)&=Ae^{\\alpha_{1}t}+Be^{\\alpha_{2}t},\\ \\left(A,B\\right)\\in\\mathbb{R}^{2}\\\\\n",
    "&=Ae^{\\left(-\\lambda+\\sqrt{\\lambda^{2}-\\omega^{2}_{0}}\\right)t}+Be^{\\left(-\\lambda-\\sqrt{\\lambda^{2}-\\omega^{2}_{0}}\\right)t}\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "Pour des valeurs réalistes de $A$ et $B$, la courbe serait la suivante:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/fZzWU5r5zJ9ewLwmXyluNlk4gRTgSA3EHelHHB4Y5N3fvJ//Wt/On7Qu5oarn0VDxsnVbDJxAilAfa0TSK7+gUHe+fX7+MGD2/i7K87i7Zee7jvbmk1CTiAFcA3kqEOHB/jLr9zHnQ9v5wMvP4drLjkt7ZDMLCVOIAXI7USfzAYGg3d+bT13PrydG1c9ize+YGnaIZlZisb3AbkTlJuwsv7pBw/zow3b+MDLz3HyMDMnkEIM1UAOTeIE8m+/fIov/OIp3vTCpW62MjPACaQgk70P5K6Ht3PD9zbysuXz+YdXLE87HDOrEE4gBWiYxH0gW7r287ffWM/yhTP45GtXUOsr8c0s4QRSgPra7PUNk60G0j8wyF9//T4i4F9ffwFT6z3mwsyO8jdCASZrE9bHfvwY9z3Tzadefz5L5vhuumZ2rFRqIJJmS1ojaVPys3mEcquTMpskrc5Z/hFJWyTtLUe8R4fxTp7H2v7ssU4++7MneP1FS3jFuQvTDsfMKlBaTVjXAXdFxDLgrmT+GJJmA9cDFwEXAtfnJJrvJsvKYrLVQPYc7Oe933qAM+dP5x/daW5mI0grgawCbk2mbwWuzlPmCmBNRHRFxG5gDXAlQET8JiI6yhEoTL7rQD7248fYvucg//Lqc33zSDMbUVoJZH5OAtgGzM9TZhGwJWe+LVk2KpKulbRO0rrOzs7RR8rkug5k/ZZubv31Zt74/FM4f0nelkUzM6CEneiS7gROzrPq/bkzERGSolRxRMTNwM0Ara2tRR1nsgzj7R8Y5H3ffpCTmhr4uyvOSjscM6twJUsgEbFypHWStktaEBEdkhYAO/IU2wpcmjPfAtw9rkEWaLI0YX3xl0/xcEcvn/3T59LUWJd2OGZW4dJqwrodGBpVtRr4Tp4ydwCXS2pOOs8vT5aVXU2NyNRoQjdhde3r4//c9TgvPfskrnhWvoqjmdmx0kogNwEvk7QJWJnMI6lV0ucBIqILuBFYm7xuSJYh6X9KagOmSmqT9MFSB1yfqZnQNZBP//Rx9vUd5n1Xne1ne5hZQVK5kDAidgGX5Vm+DrgmZ/4W4JY85d4DvKeUMQ43kRNI2+79fOnXT/OaCxazbH5T2uGYWZXwrUwKVF87cRPIx9c8hgR/87JlaYdiZlXECaRA9ZmaCTkK6+GOXv7zvq286eKlLJg5Je1wzKyKOIEUaKI2YX3sx4/S1JDh7S85I+1QzKzKOIEUqL62ZsKNwnp02x7ufHgH11xyGjOnetiumY2OE0iBGiZgE9bNP3+SKXW1/NkLTkk7FDOrQk4gBco2YU2cu/G2dx/gO+u38toLFzNran3a4ZhZFXICKdBE6wO55RdPEcBbX3Rq2qGYWZVyAilQfe3EacLq2d/P1+55hleeu4CWZj8oysyK4wRSoIlUA/nyb59mX98A17749LRDMbMq5gRSoPpM7YRIIP0Dg9z6q81csmwuyxfOSDscM6tiTiAFmihXov/kkR3s2HOIP3vB0rRDMbMq5wRSoIlyJfrX7nmG+TMa+IOz5qUdiplVOSeQAjVkqv9Cwrbd+/nZY538SetiMrX+1ZvZ2PhbpEAToRP9trXZJwT/8fMWpxyJmU0ETiAFGhrGG1Gyp++W1OGBQb6xbgsvOXOeh+6a2bhwAilQfaaGCDg8WJ0J5KePdrK99xCvu3BJ2qGY2QThBFKg+kx1Pxf96/c8w0lNDbz07JPSDsXMJggnkALV11ZvAtm59xB3P9bJqy9ooc6d52Y2TvxtUqAjNZAqHMr7w4e2MTAYrFqxMO1QzGwCSSWBSJotaY2kTcnP5hHKrU7KbJK0Olk2VdL3JT0iaYOkm8oRczU3YX13fTvLTprOWX7euZmNo7RqINcBd0XEMuCuZP4YkmYD1wMXARcC1+ckmo9GxNnA+cDFkq4qdcANSQKptmtBOnoOcM/mLl513kIkpR2OmU0gaSWQVcCtyfStwNV5ylwBrImIrojYDawBroyI/RHxU4CI6AN+B7SUOuBq7QP5/gMdALziPDdfmdn4SiuBzI+IjmR6GzA/T5lFwJac+bZk2RGSZgGvJFuLyUvStZLWSVrX2dlZdMANdUM1kOp6qNTt97fznEUzOXXutLRDMbMJpmQJRNKdkh7K81qVWy6yV+aN+uIKSRnga8D/jognRyoXETdHRGtEtM6bV/z9nxoztQAc7K+eGsjmnft4oK2HV7n2YWYlkCnVjiNi5UjrJG2XtCAiOiQtAHbkKbYVuDRnvgW4O2f+ZmBTRHxi7NGeWENdkkCqqAby3fvbAXj5uQtSjsTMJqK0mrBuB1Yn06uB7+QpcwdwuaTmpPP88mQZkj4MzAT+pvShZjUONWH1V1ECeaCdC5fOZuGsKWmHYmYTUFoJ5CbgZZI2ASuTeSS1Svo8QER0ATcCa5PXDRHRJakFeD+wHPidpPWSril1wI1JDaRaRmFt3rmPx7bv5arnnJx2KGY2QZWsCet4ImIXcFme5euAa3LmbwFuGVamDSj7eNShBHKwSmogdz68HYCV5+Qbn2BmNna+Er1Ajcl1INXSiX7nw9s5a34Ti2f7zrtmVhpOIAWqphpIz/5+1m7ezcrlvnGimZWOE0iBjiaQyq+B3P3YDgYGg8vcfGVmJeQEUqDaGlFXq6oYxnvnwzuYO72eFS2z0g7FzCYwJ5BRaMzUVnwTVv/AIHc/uoOXnn0SNTW+95WZlY4TyCg01NVWfBPW2s1d7Dl42M1XZlZyTiCj0FhXU/EXEt65cQf1mRouWTY37VDMbIJzAhmFxrraiu4DiQjuemQ7F58+h6n1qVziY2aTiBPIKDTW1VR0E9bTu/bz9K79fu65mZWFE8goVHon+i8e3wnAi5YVf9dhM7NCOYGMQmNdZSeQXz6+k0WzprB0jq8+N7PScwIZhUpuwhoYDH71xC4uPmOOH11rZmXhBDIKDRXcif7Q1h56DvS7+crMysYJZBQaM7UcqtAayFD/xwtPn5NyJGY2WTiBjEK2CasyayC/fHwn5yyYwdzpDWmHYmaThBPIKFRqJ/qBvgHWbd7Ni85w7cPMyscJZBQa62o4WIFPJFy7uYu+gUH3f5hZWTmBjEJjppaBwaB/oLKSyC8f30l9bQ3PW9qcdihmNomkkkAkzZa0RtKm5Gfebz5Jq5MymyStzln+I0n3S9og6bOSassRd6U+VOq/N+3kuafM8u1LzKys0qqBXAfcFRHLgLuS+WNImg1cD1wEXAhcn5No/jgizgOeDcwDXlOOoBvrKu+xtrv39bGxo5eLT/fNE82svNJKIKuAW5PpW4Gr85S5AlgTEV0RsRtYA1wJEBG9SZkMUA9ESaNNNFRgDWTt5i4Anu/hu2ZWZmklkPkR0ZFMbwPyPbxiEbAlZ74tWQaApDuAHcAe4FslivMYQ01YhyroYsK1m7uoz9RwbsvMtEMxs0mmZI3mku4ETs6z6v25MxERkkZdg4iIKyQ1Al8BXkq2hpIvjmuBawGWLFky2sMcozFTeU1Y92zezYqWWTRkytINZGZ2RMlqIBGxMiKenef1HWC7pAUAyc8deXaxFVicM9+SLMs9xkHgO2SbxEaK4+aIaI2I1nnzxjbMtdI60ff3HWbD1h6ed6pHX5lZ+aXVhHU7MDSqajXZJDDcHcDlkpqTzvPLgTskTc9JPhng5cAjZYg5J4FURg3kvme6OTwYPG/p7LRDMbNJKK0EchPwMkmbgJXJPJJaJX0eICK6gBuBtcnrhmTZNOB2SQ8A68nWXj5bjqCPjsKqjBrIPU91USO44BTXQMys/FK5cCAidgGX5Vm+DrgmZ/4W4JZhZbYDzyt1jPkcqYFUSCf62s1dnH3yDJoa69IOxcwmIV+JPgqNmcppwuofGOS+Z7q58FQ3X5lZOpxARqGSmrA2tPdyoH/A/R9mlhonkFGopAsJ1z6VvYDQI7DMLC1OIKMwVAM5VAF35L1ncxdL50zlpKbGtEMxs0nKCWQU6mtrkNKvgQwOBus2d7n5ysxS5QQyCpJozKT/UKknd+5j9/5+JxAzS1VBw3iTW4a8ArgEWAgcAB4Cvh8RG0oXXuXJPtY23Sas+57ZDcBzT5mVahxmNrmdMIFI+hDZ5HE38FuyF+41AmcCNyXJ5V0R8UAJ46wYlfBY2/VbumlqzHDa3OmpxmFmk1shNZB7IuL6EdZ9XNJJwNjuUlhFGutqU3+s7fot3ZzXMouaGqUah5lNbifsA4mI7wNI+r2HNkl6TUTsSK4gnxQaMjWp1kAO9A3wyLY9rFg8K7UYzMxgdJ3o7ytw2YSWdhPWQ+09DAyGE4iZpa6QPpCrgD8EFkn63zmrZgCHSxVYpZpaX8uBvvQSyPpnugFYsWRWajGYmUFhfSDtwL3Aq5KfQ/YAf1uKoCrZ1PoMu/cfSO34923ZTUvzFOZOb0gtBjMzKCCBRMT9wP2SvhIR/WWIqaJNa6hlf196Fa/1z3TzXN++3cwqwAn7QCR9V9IrR1h3mqQbJL1l/EOrTFPrM+xPqQlrR+9B2nsOcv4SJxAzS18hTVhvA/4H8AlJXUAn2etAlgJPAJ9KHlM7KUytr2X/oXRqIPdt6QZwB7qZVYRCmrC2Ae8B3iNpKbCA7JXoj0XE/tKGV3mm1deyv3+AwcEo+3UY67d0U1crnrVwRlmPa2aWz6ieSBgRm4HNJYmkSkxtyBCRfSrh1PryPtBx/TPdnLNgxpEnI5qZpamQPpBfJD/3SOrNee2R1Fv6ECvLtPrsl/e+Q+XtBxkYDB5o63bzlZlVjEKuRH9R8rMpImbkvJoioqi2FEmzJa2RtCn5mbdXWNLqpMwmSavzrL9d0kPFxFCsoVpHua8FeaJzL/v6BpxAzKxipHU79+uAuyJiGXBXMn8MSbOB64GLgAuB63MTjaT/F9hbnnCPmjpUAynzUN6HtvYA8JxFM8t6XDOzkaSVQFYBtybTtwJX5ylzBbAmIroiYjewBrgSQNJ0siPDPlz6UI81tSFbAyn3tSAb2ntpyNRw6txpZT2umdlI0kog8yOiI5neBszPU2YRsCVnvi1ZBnAj8DHghKPAJF0raZ2kdZ2dnWMIOSutPpCN7b2cvWAGmVo/A8zMKkPJvo0k3SnpoTyvVbnlIiKAGMV+VwCnR8R/FlI+Im6OiNaIaJ03b96o3kM+Q30g5byYMCLY0N7j4btmVlFKNg41IlaOtE7SdkkLIqJD0gKyD6kabitwac58C9mHWr0AaJW0mWz8J0m6OyIupQymNWRrIOVswmrbfYDeg4dZvsAJxMwqR1rtIbcDQ6OqVgP5rmS/A7hcUnPSeX45cEdEfCYiFkbEUuBFZC9ovLQMMQMw5UgnevlqIBs7sqOlXQMxs0qSVgK5CXiZpE3AymQeSa2SPg8QEV1k+zrWJq8bkmWpmjbUhFXG25lsaO+lRnD2yU4gZlY5ynspdSIidgGX5Vm+DrgmZ/4W4Jbj7Gcz8OwShDiiKXUp1EDaezht3vQjtR8zs0rgIT2jVFOj5KFS5auBbGzvdfOVmVUcJ5AiTK3PlK0GsntfH+09B51AzKziOIEUoZy3dN/Qnu1AX77AV6CbWWVxAinC1PrastVANnZkb2HiGoiZVRonkCJMa8iU7WaKG9p7WTizkeZp9WU5nplZoZxAipCtgZSvCWu5ax9mVoGcQIowrT7D/jLcC+tA3wBPdu5l+UL3f5hZ5XECKUK5aiCPbOtlMNz/YWaVyQmkCFMbastyM8WjI7CcQMys8jiBFGFafaYsN1Pc2NHLzCl1tDRPKfmxzMxGywmkCFPrMxzsH2RgsOC70BdlQ3svyxfMQFJJj2NmVgwnkCKU45buhwcGeaTDtzAxs8rlBFKEoZsalrIf5Mmd+zh0eNBDeM2sYjmBFGFaGZ5KuLF96BkgHsJrZpXJCaQIU488F710TVgb2nuoz9Rw+rxpJTuGmdlYOIEUYVpDtgZS2gTSy9knN5Gp9a/IzCqTv52KMH0ogZSoEz0i2OgOdDOrcE4gRZgxpQ6A3gOlSSDtPQfp3t/vW5iYWUVzAinCjMZsDaT3YH9J9r9ha/YW7r4C3cwqWSoJRNJsSWskbUp+No9QbnVSZpOk1TnL75b0qKT1yeuk8kUPTY1DNZDSJJCNHb1IcM6CppLs38xsPKRVA7kOuCsilgF3JfPHkDQbuB64CLgQuH5YonlDRKxIXjvKEfSQ+kwNU+pq6T1YmiasDe29nDZ3GlOT4cJmZpUorQSyCrg1mb4VuDpPmSuANRHRFRG7gTXAleUJ78SaGjOlq4G097r/w8wqXloJZH5EdCTT24D5ecosArbkzLcly4Z8MWm++gcd52ZRkq6VtE7Sus7OzjEHPmTGlLqS9IF07+9ja/cBj8Ays4pXsjYSSXcCJ+dZ9f7cmYgISaO9K+EbImKrpCbgP4A3Av+er2BE3AzcDNDa2jpudz+c0ZgpySiso1egO4GYWWUrWQKJiJUjrZO0XdKCiOiQtADI14exFbg0Z74FuDvZ99bk5x5JXyXbR5I3gZTKjCl1dO3rG/f9+hkgZlYt0mrCuh0YGlW1GvhOnjJ3AJdLak46zy8H7pCUkTQXQFId8ArgoTLEfIwZjXUl6QPZ2NHLyTMamTO9Ydz3bWY2ntJKIDcBL5O0CViZzCOpVdLnASKiC7gRWJu8bkiWNZBNJA8A68nWVD5X7jcwY0qGPSUYhbWhvcfNV2ZWFVIZJxoRu4DL8ixfB1yTM38LcMuwMvuAC0od44nMaMx2okfEuD3w6WD/AE907uOKZ+XrOjIzqyy+Er1IM6bU0T8QHOwfHLd9PrptDwOD4RqImVUFJ5AiNZXgdiYb/AwQM6siTiBFmlGC25lsaO+hqTFDS/OUcdunmVmpOIEU6cgdecexBrKxo5flC2aMW5+KmVkpOYEU6cgdecfpYsKBweCRjj1uvjKzquEEUqTxroE8tXMvB/oHWO4OdDOrEk4gRRrvPpANvoWJmVUZJ5AiHR2FNT5NWBvbe6mvreGMk6aPy/7MzErNCaRIjXW1NGRqxq0Ja0N7L2eePJ26Wv9KzKw6+NtqDJoa68alEz0isrcwWeAOdDOrHk4gYzBjSmZcaiDbeg+ye38/z1rk/g8zqx5OIGMwXnfk3bDVt3A3s+rjBDIGM6aMUwJp70WCc5xAzKyKOIGMwdxp9ewah4dKbezo4dQ505jWkMrNkc3MiuIEMgZzpteza+/YE8iG9l7O8fUfZlZlnEDGYM70Bg70D7DvUPEjsXr299O2+4AvIDSzquMEMgZzptUDjKkWsrHDt3A3s+rkBDIGc5Pnlu/cd6jofWxo7wE8AsvMqo8TyBgMJZAx1UDaezmpqYF5TQ3jFZaZWVmkkkAkzZa0RtKm5GfzCOVWJ2U2SVqds7xe0s2SHpP0iKRXly/6o+ZMH2rCKr4GsrGj1/0fZlaV0qqBXAfcFRHLgLuS+WNImg1cD1wEXAhcn5No3g/siIgzgeXAz8oS9TCzkz6QnUUmkAN9A2zasdf9H2ZWldJKIKuAW5PpW4Gr85S5AlgTEV0RsRtYA1yZrHsL8M8AETEYETtLG25+jXW1NDVk2FlkE9bGjl4GBoNzW5xAzKz6pJVA5kdERzK9DZifp8wiYEvOfBuwSNKsZP5GSb+T9E1J+bYHQNK1ktZJWtfZ2TkesR9jzvTiLyZ8sK0bgHNbZo1fQGZmZVKyBCLpTkkP5Xmtyi0XEQHEKHadAVqAX0XEc4FfAx8dqXBE3BwRrRHROm/evGLeynHNmd5QdB/IA1t7mNfUwPwZ7kA3s+pTsntnRMTKkdZJ2i5pQUR0SFoA7MhTbCtwac58C3A3sAvYD3w7Wf5N4K3jEXMx5k6vZ/PO/UVt+2BbD+cumomkcY7KzKz00mrCuh0YGlW1GvhOnjJ3AJdLak46zy8H7khqLN/laHK5DNhY2nBHNmd6Q1Gd6HsPHebxzr1uvjKzqpVWArkJeJmkTcDKZB5JrZI+DxARXcCNwNrkdUOyDOC9wAclPQC8EXhXmeM/Yu60err29zEwOJpWONiwtYcI3IFuZlUrldu/RsQusjWH4cvXAdfkzN8C3JKn3NPAi0sZY6HmTG8gAnbv7ztyYWEhHtyavQL92YucQMysOvlK9DE6ejHh6EZiPdDWw8KZjb4C3cyqlhPIGB29ncno+kEe3NrDc9x8ZWZVzAlkjE5KahDbeg8WvE3PgX6e2rnPHehmVtWcQMZo4awpAGzpOlDwNhuS/o/nuP/DzKqYE8gYNdbVMn9GA1t2F34tyANOIGY2ATiBjIPFzVPZ0lV4AnmwrYfFs6fQnNyM0cysGjmBjIPFs6fStrvwJqz727o5d9Gs0gVkZlYGTiDjYHHzFDp6DtA/MHjCsjt6D9K2+wArFs8qfWBmZiXkBDIOWmZPZTCgvfvEtZC1m3cD8LxTZ5c6LDOzknICGQeLm6cChY3EWru5iyl1tX4KoZlVPSeQcbB4djKUt4CRWGs3d3H+klnU1frUm1l187fYOFgwcwqZGp1wJNaeg/083NFL61I3X5lZ9XMCGQe1NWLhrClsOcFIrPue6WYw4EInEDObAJxAxsni2VNOWAP5zZO7qK0R5y+ZVZ6gzMxKyAlknJw+bzqbtu857nNBfvZYJxec0sy0hlTuom9mNq6cQMbJeS2z2Nc3wOM79uZdv2PPQTa09/KSM8f/uexmZmlwAhknK5Jmqfu3dOdd//PHdgJw6VlOIGY2MTiBjJNT50yjqTHDfSMkkJ891sm8pgaWL/D1H2Y2MTiBjJOaGrFi8ay8NZD+gUH+e1MnL142D0nlD87MrARSSSCSZktaI2lT8rN5hHKrkzKbJK1OljVJWp/z2inpE2V9AyNYsXgWj27fw4G+gWOW//SRHXTv7+eqZ5+cUmRmZuMvrRrIdcBdEbEMuCuZP4ak2cD1wEXAhcD1kpojYk9ErBh6AU8D3y5f6CM7r2UWA4PBg8nzPobctm4LJzU1uP/DzCaUtBLIKuDWZPpW4Oo8Za4A1kREV0TsBtYAV+YWkHQmcBLw36ULtXAXnNJMXa34wYMdR5bt6D3ITx/t5NUXtJDx7UvMbAJJ6xttfkQMfctuA+bnKbMI2JIz35Ysy/Va4BsRMeLFF5KulbRO0rrOzs6xxHxCzdPqWbViEd9Yu4Xu/X0A/Puvn2ZgMHjNBS0lPbaZWbmVLIFIulPSQ3leq3LLJV/+I199d3yvBb52vAIRcXNEtEZE67x5pW9Cetslp3Ggf4B///XTrNvcxWd+9gSrVizktHnTS35sM7NyKtkl0RGxcqR1krZLWhARHZIWADvyFNsKXJoz3wLcnbOP84BMRNw7PhGPj7NObuLSs+bx8TWP8cm7xKJZU/jw1c9OOywzs3GX1j01bgdWAzclP7+Tp8wdwD/ljNC6HHhfzvrXcYLaR1o++Sfn8+372ni4o5c3vfBUmhrr0g7JzGzcpZVAbgJuk/RWsqOo/hhAUivwFxFxTUR0SboRWJtsc0NEdOXs44+BPyxn0IWaObWON198atphmJmVlI7T/zzhtLa2xrp169IOw8ysqki6NyJahy/3uFIzMyuKE4iZmRXFCcTMzIriBGJmZkVxAjEzs6I4gZiZWVGcQMzMrCiT6joQSZ1kL1wsxlxg5ziGU+18Po7yuTiWz8dRE+VcnBIRv3czwUmVQMZC0rp8F9JMVj4fR/lcHMvn46iJfi7chGVmZkVxAjEzs6I4gRTu5rQDqDA+H0f5XBzL5+OoCX0u3AdiZmZFcQ3EzMyK4gRiZmZFcQI5AUlXSnpU0uOSrks7njRJWizpp5I2Stog6Z1px1QJJNVKuk/S99KOJU2SZkn6lqRHJD0s6QVpx5QmSX+b/J08JOlrkhrTjmm8OYEch6Ra4NPAVcBy4HWSlqcbVaoOA++KiOXA84G/nOTnY8g7gYfTDqICfBL4UUScDZzHJD4nkhYBfw20RsSzgVrgtelGNf6cQI7vQuDxiHgyIvqArwOrUo4pNRHRERG/S6b3kP2CWJRuVOmS1AK8HPh82rGkSdJM4MXAFwAioi8iulMNKn0ZYIqkDDAVaE85nnHnBHJ8i4AtOfNtTPIvzCGSlgLnA79NOZS0fQJ4DzCYchxpOxXoBL6YNOd9XtK0tINKS0RsBT4KPAN0AD0R8eN0oxp/TiA2apKmA/8B/E1E9KYdT1okvQLYERH3ph1LBcgAzwU+ExHnA/uASdtnKKmZbGvFqcBCYJqkP003qvHnBHJ8W4HFOfMtybJJS1Id2eTxlYj4dtrxpOxi4FWSNpNt3nyppC+nG1Jq2oC2iBiqkX6LbEKZrFYCT0VEZ0T0A98GXphyTOPOCeT41gLLJJ0qqZ5sJ9jtKceUGkki28b9cER8PO140hYR74uIlohYSvaz8ZOImHD/ZRYiIrYBWySdlSy6DNiYYkhpewZ4vqSpyd/NZUzAQQWZtAOoZBFxWNJfAXeQHUVxS0RsSDmsNF0MvBF4UNL6ZNnfR8QP0gvJKsg7gK8k/2w9Cbw55XhSExG/lfQt4HdkRy/exwS8rYlvZWJmZkVxE5aZmRXFCcTMzIriBGJmZkVxAjEzs6I4gZiZWVGcQMxSlNzB9u1px2FWDCcQs3TNApxArCo5gZil6ybgdEnrJf1/aQdjNhq+kNAsRcldjb+XPDPCrKq4BmJmZkVxAjEzs6I4gZilaw/QlHYQZsVwAjFLUUTsAn4p6SF3olu1cSe6mZkVxTUQMzMrihOImZkVxQnEzMyK4gRiZmZFcQIxM7OiOIGYmVlRnEDMzKwo/xcvdbL5P2sFIAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from math import exp\n",
    "\n",
    "fsola = -3.1\n",
    "fsolb = -2.1\n",
    "constantA = 0.5\n",
    "x_pts = np.linspace(0, 9, 200)\n",
    "y_pts = []\n",
    "for x in x_pts:\n",
    "    y_pts.append(constantA * (exp(fsola * x) - exp(fsolb * x)))\n",
    "\n",
    "plt.xlabel(\"t\")\n",
    "plt.ylabel(\"i(t)\")\n",
    "plt.plot(x_pts, y_pts)\n",
    "plt.title(\"Tracé réaliste de la courbe de l'intensité\")\n",
    "plt.show()\n",
    "\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.\n",
    "On sait que $i\\left(0\\right)=A+B=0$ donc $B=-A$.\n",
    "\n",
    "$$i\\left(t\\right)=A\\left(e^{\\left(-\\lambda+\\sqrt{\\lambda^{2}-\\omega^{2}_{0}}\\right)t}-e^{\\left(-\\lambda-\\sqrt{\\lambda^{2}-\\omega^{2}_{0}}\\right)t}\\right)$$\n",
    "\n",
    "Or avec l'inductance: $L\\dfrac{di}{dt}\\left(0\\right)=-U_{0}\\iff\\dfrac{di}{dt}\\left(0\\right)=-\\dfrac{U_{0}}{L}$\n",
    "\n",
    "$$\\dfrac{di}{dt}\\left(t\\right)=A\\left(\\left(-\\lambda+\\sqrt{\\lambda^{2}-\\omega^{2}_{0}}\\right)e^{\\left(-\\lambda+\\sqrt{\\lambda^{2}-\\omega^{2}_{0}}\\right)t}-\\left(-\\lambda-\\sqrt{\\lambda^{2}-\\omega^{2}_{0}}\\right)e^{\\left(-\\lambda-\\sqrt{\\lambda^{2}-\\omega^{2}_{0}}\\right)t}\\right)$$\n",
    "\n",
    "Donc les conditions initiales nous donnent:\n",
    "\n",
    "$\n",
    "\\begin{align}\n",
    "\\dfrac{di}{dt}\\left(0\\right)&=A\\left(\\left(-\\lambda+\\sqrt{\\lambda^{2}-\\omega^{2}_{0}}\\right)+\\left(\\lambda+\\sqrt{\\lambda^{2}-\\omega^{2}_{0}}\\right)\\right)\\\\\n",
    "&=2A\\sqrt{\\lambda^{2}-\\omega^{2}_{0}}\\\\\n",
    "&=-\\dfrac{U_{0}}{L}\n",
    "\\end{align}\n",
    "$\n",
    "$$A=-\\cfrac{U_{0}}{2L\\sqrt{\\lambda^{2}-\\omega^{2}_{0}}}$$\n",
    "\n",
    "D'où l'expression finale de i:\n",
    "\n",
    "$$i\\left(t\\right)=\\dfrac{U_{0}}{2L\\sqrt{\\lambda^{2}-\\omega^{2}_{0}}}\\left(e^{\\left(-\\lambda+\\sqrt{\\lambda^{2}-\\omega^{2}_{0}}\\right)t}-e^{\\left(-\\lambda-\\sqrt{\\lambda^{2}-\\omega^{2}_{0}}\\right)t}\\right)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "lbd = 2000000 # Valeur de lambda\n",
    "lbd2 = lbd ** 2 # Lambda au carré\n",
    "mlbd_2 = -lbd * 2 # Valeur de lambda multipliée par -2\n",
    "w_02 = 81649 ** 2 # Omega au carré\n",
    "\n",
    "# Permet de calculer i_(n+2) avec i_(n+1), i_(n) et une période t\n",
    "def calculate_next(t, in0, in1):\n",
    "    return (2 - 2*lbd*t)*in1 - (1 - 2*lbd*t + t**2*w_02)*in0\n",
    "\n",
    "# Fonction d'approximation complète\n",
    "def calc_values(period, time, i0, i1):\n",
    "    n = int(time / period)\n",
    "    indexes = [0] * n\n",
    "    indexes[1] = period\n",
    "    values = [0] * n\n",
    "    values[0] = i0\n",
    "    values[1] = i1\n",
    "    for i in range(2, n):\n",
    "        values[i] = calculate_next(period, values[i - 2], values[i - 1])\n",
    "        indexes[i] = i * period\n",
    "    return indexes, values\n",
    "\n",
    "L = 0.0015 # Constante d'inductance\n",
    "\n",
    "from math import sqrt, exp\n",
    "import numpy as np\n",
    "def direct_method(t):\n",
    "    vp = sqrt(lbd2 - w_02)\n",
    "    return -1 / (2 * L * vp) * (exp((-lbd + vp) * t) - exp((-lbd - vp) * t))\n",
    "\n",
    "fig_a, aspbs = plt.subplots(1, 2)\n",
    "fig_a.subplots_adjust(wspace=1)\n",
    "\n",
    "# Il est nécessaire de fournir une période très petite étant donné la taille de l'intervalle et des grandeurs.\n",
    "Tp = 0.00000001\n",
    "idxs, vls = calc_values(Tp, 0.002, 0, -Tp / L)\n",
    "d = np.arange(0.0, 0.002, Tp)\n",
    "dv = np.vectorize(direct_method)(d)\n",
    "\n",
    "aspbs[0].plot(idxs, vls)\n",
    "aspbs[0].title.set_text(\"Courbe approximée\")\n",
    "\n",
    "aspbs[1].plot(d, dv, 'b', d, dv, 'k')\n",
    "aspbs[1].title.set_text(\"Courbe avec formule connue\")\n",
    "\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.10.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}

requirements.txt

scipy
matplotlib

RLC_exp.TXT

# t	i
0	0
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2.3438E-6	-0.0010897
3.5156E-6	-0.0015226
4.6875E-6	-0.0018443
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1.7578E-5	0.0012152
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