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Clases/Clase_para_el_pendulo.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 44,
+   "id": "d8c9cc7e-12af-41a2-a3e2-17947687b52b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 55,
+   "id": "0a9bf50c-beb0-419c-8461-08b7b11db189",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "L = np.arange(10, 32, 2)\n",
+    "dL = np.random.rand(len(L))\n",
+    "B = 0.5\n",
+    "alpha = 0.3\n",
+    "T0 = T = B*L**alpha\n",
+    "T = B*(L+dL)**alpha"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 56,
+   "id": "cafe1b32-cfac-4005-888d-75cb295b539b",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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pspnZlUYZ9MvA9o7lbcDZXhtHxDwwDzA7O9vzF4JdrlZzwJtZf6McunkWuEnSjZKqwL3AYyPcn5mZdTHwjF7SMSABtkhaBh4ENgFExCFJPw0sAD8BXJT0aWBHRPxQ0v3Ak0AFOBwRL4zkuzAzs54GBn1E7B/Q/kekwzLd2h4HHr+60szMLA/+z1gzs5Jz0JuZlZyD3sys5Bz0ZmYl56A3Mys5B72ZWck56M3MSs5Bb2ZWcg56M7OSc9CbmZWcg97MrOQc9GZmJeegz0FzqcnBpw/SXGoWXYqZ2Y8Z5cQj14TmUpPdR3fTareoVqrUD9SpbfdMIGY2PnxGv0aNxQatdot2tGm1WzQWG0WXZGZ2GQf9GiUzCdVKlYoqVCtVkpmk6JLMzC7joZs1qm2v8Rs76zx6qsE9OxMP25jZ2BlmKsHDwAeAlYi4uUu7gH8N3A38CPh4RPx+1rYIvAG0gQsRMZtf6eOh2YRP31Oj1arxdBX+St2TdZvZeBlm6OYIsKdP+17gpuxrDvj8Fe13RsRtZQx5gEYDWi1ot9PHRqPoiszMLjcw6CPiJPB6n032AUcj9Qzwdkk35FXguEsSqFahUkkfk6ToiszMLpfHGP1WYKljeTlb9yoQwFOSAvjtiJjv9SaS5kj/ImB6ejqHstZHrQb1enomnyQetjGz8ZNH0KvLusgeb4+Is5LeAXxN0ovZXwg//oL0l8A8wOzsbHTbZlzVag54MxtfeVxeuQxs71jeBpwFiIhLjyvACWBXDvszM7NVyCPoHwMOKPVzwJ9ExKuSNku6DkDSZuAu4HQO+zMzs1UY5vLKY0ACbJG0DDwIbAKIiEPA46SXVp4hvbzyl7KXvhM4kV59yUbgyxHx1ZzrNzOzAQYGfUTsH9AewH1d1r8M3Hr1pZmZWR58CwQzs5Jz0JuZlZyD3sys5Bz0ZmYl56A3Mys5B72ZWcmVKug9d6uZ2Y8rzcQjnrvVzKy70pzRe+5WM7PuShP0nrvVzKy70gzd1LbXqB+o01hskMx47lYzs0tKE/SQhr0D3szscqUZujEzs+4c9GZmJeegNzMrOQe9mVnJDQx6SYclrUjqOg1gNoXgv5F0RtLzknZ2tO2R9FLW9kCehZuZ2XCGOaM/Auzp074XuCn7mgM+DyCpAjySte8A9kvasZZizcxs9QYGfUScBF7vs8k+4GikngHeLukGYBdwJiJejogWcDzbdmSaTTh4MH00M7NUHtfRbwWWOpaXs3Xd1r+315tImiP9i4Dp6elVF9Fswu7d0GpBtQr1OtR8Sb2ZWS4fxqrLuuizvquImI+I2YiYnZqaWnURjUYa8u12+thorPotzMxKKY8z+mVge8fyNuAsUO2xfiSSJD2Tv3RGnySj2pOZ2WTJI+gfA+6XdJx0aOZPIuJVSeeAmyTdCLwC3At8OIf9dVWrpcM1jUYa8h62MTNLDQx6SceABNgiaRl4ENgEEBGHgMeBu4EzwI+AX8raLki6H3gSqACHI+KFEXwP/1+t5oA3M7vSwKCPiP0D2gO4r0fb46S/CMzMrCD+z1gzs5Jz0JuZlZyD3sys5Bz0ZmYl56A3Mys5pRfNjJfsGvw/vMqXbwF+kGM5eXFdq+O6Vsd1rU4Z6/pLEdH1tgJjGfRrIWkhImaLruNKrmt1XNfquK7Vudbq8tCNmVnJOejNzEqujEE/X3QBPbiu1XFdq+O6Vueaqqt0Y/RmZna5Mp7Rm5lZBwe9mVnJTUzQSzosaUXS6Y51PyXpa5K+mz3+ZI/X7pH0kqQzkh5Yh7r+haQXJT0v6YSkt/d47aKkb0l6TtLCOtT1a5Jeyfb3nKS7e7x2vY/X73bUtCjpuR6vHeXx2i7p65K+LekFSf8oW19oH+tTV6F9rE9dhfaxPnUV2sck/XlJ/0PSN7O6/km2fn36V0RMxBfwPmAncLpj3T8HHsiePwA83OV1FeB7wM+Qznr1TWDHiOu6C9iYPX+4W11Z2yKwZR2P168Bvzrgdet+vK5o/5fA5wo4XjcAO7Pn1wHfAXYU3cf61FVoH+tTV6F9rFddRfcx0qlV35Y93wT8d+Dn1qt/TcwZfUScBF6/YvU+4IvZ8y8CH+zy0l3AmYh4OSJawPHsdSOrKyKeiogL2eIzpNMorqsex2sY6368LpEk4O8Bx/La37Ai4tWI+P3s+RvAt0knuC+0j/Wqq+g+1ud4DWPdj9el9qL6WKTezBY3ZV/BOvWviQn6Ht4ZEa9C+gMG3tFlm63AUsfyMsN3yDx8AniiR1sAT0k6JWluneq5P/tz/3CPPxOLPF5/Hfh+RHy3R/u6HC9JM8BfJT3rGps+dkVdnQrtY13qGos+1uN4FdbHJFWyIaMV4GsRsW79a9KDfhjqsm5drimV9FngAvA7PTa5PSJ2AnuB+yS9b8QlfR54F3Ab8Crpn7BXKux4Afvpf6Y18uMl6W3Ao8CnI+KHw76sy7pcj1mvuoruY13qGos+1ufnWFgfi4h2RNxG+tfXLkk3D/nSNR+vSQ/670u6ASB7XOmyzTKwvWN5G3B21IVJ+hjwAeAjkQ20XSkizmaPK8AJ0j/RRiYivp91tovAv+2xv6KO10bg7wC/22ubUR8vSZtIw+F3IuIr2erC+1iPugrvY93qGoc+1ud4Fd7Hsvf+Y6AB7GGd+tekB/1jwMey5x8D/lOXbZ4FbpJ0o6QqcG/2upGRtAf4DPC3I+JHPbbZLOm6S89JP1w73W3bHOu6oWPxQz32t+7HK/MLwIsRsdytcdTHKxu7/XfAtyPiX3U0FdrHetVVdB/rU1ehfazPzxEK7GOSppRdGSXpL1yqhfXqX3l/ujyqL9I/t14FzpP+hvskcD1QB76bPf5Utu1fBB7veO3dpJ++fw/47DrUdYZ0TO257OvQlXWRfoL+zezrhXWq60vAt4Dns45ywzgcr2z9EeBTV2y7nsfrDtI/h5/v+LndXXQf61NXoX2sT12F9rFedRXdx4BbgP+Z1XWa7Kqf9epfvgWCmVnJTfrQjZmZDeCgNzMrOQe9mVnJOejNzErOQW9mVnIOejOzknPQm5mV3P8DnQHJOeZxDckAAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.figure()\n",
+    "plt.plot(L, T0, 'b.')\n",
+    "plt.plot(L, T, 'g.')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 57,
+   "id": "7d536043-8efb-4a8f-9017-7b9b13c8ea1a",
+   "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": [
+    "X = np.log(L)\n",
+    "Y = np.log(T)\n",
+    "\n",
+    "plt.figure()\n",
+    "plt.plot(X, Y, 'g.')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6c99b9ca-c8c1-43ae-988f-6430c66aca0d",
+   "metadata": {},
+   "source": [
+    "## Ajuste lineal"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 60,
+   "id": "3ded9ca3-c33a-4b0f-8b02-04dc38c6fca6",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.28504042495634563 -0.6423000064800591\n"
+     ]
+    }
+   ],
+   "source": [
+    "alpha_exp, C_exp = np.polyfit(X,Y, 1)\n",
+    "print(alpha_exp, C_exp)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 61,
+   "id": "7d0c0abf-9ba7-43db-97bd-b8c0867e093e",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.5260810416785282"
+      ]
+     },
+     "execution_count": 61,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "np.exp(C_exp)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "c5e3186b-dd09-4813-a21c-48e980741cb2",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "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": "3.8.8"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}