f3/i2_Pendulo_amortiguamiento.ipynb

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   "source": [
    "<h1 align=\"center\">Obtención del coeficiente de amortiguamiento</h1>\n",
    "<div align=\"right\">David A. Miranda, Ph.D<br>2020</div>\n",
    "\n",
    "Los datos obtenidos en el experimento se pueden modelar con la siguiente ecuación:\n",
    "$$\\theta(t) = \\theta_0 e^{-\\beta ( t - t_0 )} sin[\\omega (t - t_0)]$$\n",
    "Donde $\\theta_0$ es la amplitud de la oscilación cuando inicia el movimiento; $t_0$, el tiempo en que inicia el movimiento; $\\beta$, el coeficiente de atenuación y $\\omega = 2\\pi / T $, la frecuencia angular, la cual está asociada con el periodo $T$ de la onda no amortiguada."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Importa las librerías a utilizar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "tpcgzKu7W8eq"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Carga los datos obtenidos en el laboratorio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "Ide5ibZEcPNI"
   },
   "outputs": [],
   "source": [
    "time = [\n",
    " 4.20,\n",
    " 5.00,\n",
    " 5.84,\n",
    " 6.70,\n",
    " 7.50,\n",
    " 8.30,\n",
    " 9.10,\n",
    " 9.90,\n",
    "10.80,\n",
    "] # Segundo\n",
    "angle = [\n",
    " 10,\n",
    "-10,\n",
    "  9,\n",
    " -8,\n",
    "  8,\n",
    " -6,\n",
    "  6,\n",
    " -6,\n",
    "  5,\n",
    "] # Grados"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Método 1: obtención del coeficiente de atenuación a partir de dos puntos\n",
    "\n",
    "Dado que la amplitud de la oscilación $A$ disminuye en el tiempo siguiendo una función exponencial, tal que,\n",
    "\n",
    "$$A(t) = \\theta_0 e^{-\\beta (t-t_0)}$$\n",
    "\n",
    "Entonces, se puede obtener $\\beta$ a partir de los datos para dos tiempos conocidos, $t_0$ y $t_1$,\n",
    "\n",
    "$$\\frac{A(t_1)}{A(t_0)} = e^{-\\beta (t_1-t_0)}$$\n",
    "\n",
    "Al despejar $\\beta$ se obtiene,\n",
    "\n",
    "$$\\beta = \\frac{-1}{t_1-t_0} ln\\left[\\frac{A(t_1)}{A(t_0)}\\right]$$\n",
    "\n",
    "Note que este es el método más simple, no el más preciso.\n",
    "\n",
    "Ver descripción en este [video](https://youtu.be/M1_4gJecyjc)."
   ]
  },
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    "outputId": "fe9f309d-12ee-471e-b453-b045ee7bfba0"
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "T = 1.65 # s\n",
    "β = 0.1050223001 # 1/s\n",
    "m = 1 # kg\n",
    "θo = max(np.abs(angle)) # Grados\n",
    "t = np.linspace(min(time), max(time), 1000)\n",
    "t0 = min(t)\n",
    "θ_model = θo*np.exp(-β*(t-t0))*np.cos(2*np.pi*(t - t0)/T)\n",
    "\n",
    "plt.figure(dpi=120)\n",
    "plt.plot(time, angle, 'o')\n",
    "plt.plot(t, θ_model, 'b:')\n",
    "plt.xlabel('Tiempo [s]')\n",
    "plt.ylabel('Angulo en grados')\n",
    "_ = plt.title(r'$\\beta = %0.3f$ $[s^{-1}]$, $\\gamma = %0.3f$ $[N s/m]$' % (β, 2*m*β))\n",
    "_ = plt.axis([t0, max(time), 1.1*min(angle), 1.1*max(angle)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4. Método 2: obtención del coeficiente de atenuación por linealización de los datos\n",
    "\n",
    "En este segundo método, mucho más preciso que el anterior, se linealiza la ecuación que describe el cambio en la amplitud $A(t)$ de la oscilación.  Para ello se realiza el siguiente cambio de variable:\n",
    "\n",
    "$$y = - ln\\left|\\frac{\\theta(t)}{\\theta_0}\\right|$$\n",
    "\n",
    "$$x = t - t_0$$\n",
    "\n",
    "A continuación, se grafica $y$ en función de $x$, lo cual tendrá una tendencia lineal dado por,\n",
    "\n",
    "$$y = \\beta x$$\n",
    "\n",
    "A partir de estos datos se obtienen la pendiente, que será el coeficiente de atenuación $\\beta$. \n",
    "\n",
    "Ver descripción en este [video](https://youtu.be/Khrhk-4LTJ0)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "T = 2*np.mean(np.diff(time)) # s\n",
    "t0 = min(t)\n",
    "θo = max(np.abs(angle)) # Grados\n",
    "x = time - t0\n",
    "y = - np.log( np.abs(angle) / θo)\n",
    "## Filtrado de datos para dejar solo datos válidos ##\n",
    "k_finite = np.isfinite(x) & np.isfinite(y) # Encuentra los valores finitos (diferntes de NaN e Inf)\n",
    "x = x[k_finite]\n",
    "y = y[k_finite]\n",
    "t_fit = np.array(time)[k_finite] - t0\n",
    "#####################################################\n",
    "p = np.polyfit(x, y, 1)\n",
    "β = p[0] # 1/s\n",
    "p[1] = 0 # garantiza el cruce por cero\n",
    "m = 1 # kg\n",
    "θo = max(angle) # Grados"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = np.linspace(min(time), max(time), 1000)\n",
    "θ = θo*np.exp(-β*(t-t0))*np.cos(2*np.pi*(t - t0)/T)\n",
    "\n",
    "correlation_matrix = np.corrcoef(y, np.polyval(p, t_fit))\n",
    "R = correlation_matrix[0, 1]**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "label = 'β = %0.3f [1/s] \\nR = %0.2f' % (β, R) \n",
    "\n",
    "x_model2 = np.linspace(0.8*min(time), 1.1*max(time), 10) - t0\n",
    "y_model2 = np.polyval(p, x_model2)\n",
    "\n",
    "plt.figure(dpi=120)\n",
    "plt.plot(x, y, 'ok')\n",
    "plt.plot(x_model2, y_model2, 'k', label=label)\n",
    "plt.xlabel(r'$x = t - t_0$ [s]')\n",
    "_ = plt.ylabel(r'$y = - ln\\left|\\theta(t) / \\theta_0\\right| $')\n",
    "plt.legend()\n",
    "try:\n",
    "    _ = plt.axis([0, max(x_model2), min(y_model2), max(y_model2)])\n",
    "except:\n",
    "    pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.figure(dpi=120)\n",
    "plt.plot(time, angle, 'o')\n",
    "plt.plot(t, θ, 'b:')\n",
    "plt.xlabel('Tiempo [s]')\n",
    "plt.ylabel('Angulo en grados')\n",
    "_ = plt.title(r'$\\beta = %0.3f$ $[s^{-1}]$, $\\gamma = %0.3f$ $[N s/m]$' % (β, 2*m*β))\n",
    "_ = plt.axis([t0, max(time), 1.1*min(angle), 1.1*max(angle)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "End!"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "name": "Untitled0.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.6-final"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}