Phase1_NonLinearOscillatorSimulation.ipynb

{
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  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "XfagyVMvwgGn"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "from matplotlib import pyplot as plt\n",
        "from scipy.integrate import odeint\n",
        "import pandas as pd"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Constants\n",
        "N = 2\n",
        "mu_m = 0.011\n",
        "mu_s = 0.00016\n",
        "g = 9.81\n",
        "L = 0.22\n",
        "Omega = np.sqrt(g/L)\n",
        "omega = 8.61\n",
        "beta = 0.0005\n",
        "x0 = beta*g/(omega**2)\n",
        "theta0 = 1"
      ],
      "metadata": {
        "id": "6ryH_2zLgwb2"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def find_freq(y):\n",
        "  av_l = np.average(y)\n",
        "  start = None\n",
        "  stop = None\n",
        "  for i in range(1,len(y)-1):\n",
        "    if (y[i]>av_l and y[i+1]<=av_l) or (y[i]<=av_l and y[i+1]>av_l):\n",
        "      start = i\n",
        "      break\n",
        "  for i in range(start+1,len(y)-1):\n",
        "    if (y[i]>av_l and y[i+1]<=av_l) or (y[i]<=av_l and y[i+1]>av_l):\n",
        "      stop = i \n",
        "      break\n",
        "  if (start ==None or stop == None):\n",
        "    return None\n",
        "  else :\n",
        "    return(1/(t[stop]-t[start]))"
      ],
      "metadata": {
        "id": "W2K0qpoWMlBT"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def find_peaks(y):\n",
        "  av_l = np.average(y)\n",
        "  peaks = []\n",
        "  for i in range(1,len(y)-1):\n",
        "    if(y[i]>=y[i-1] and y[i]>=y[i+1]):\n",
        "      peaks.append(y[i])\n",
        "  peaks = np.array(peaks)\n",
        "  peaks = peaks - np.ones(len(peaks))*av_l\n",
        "  return peaks"
      ],
      "metadata": {
        "id": "NhwxN9dWkFzE"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def Amplitude(y):\n",
        "   peaks = find_peaks(y)\n",
        "   return np.average(peaks[-10:])"
      ],
      "metadata": {
        "id": "Dv4LClvnlsLs"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "phis = np.zeros(N)\n",
        "phisdot = np.zeros(N)\n",
        "def odes(z, t):\n",
        "    PHI = z[0]\n",
        "    PHI_dot = z[1]\n",
        "    for j,i in enumerate(range(0,2*N,2)):\n",
        "      phis[j] = z[i+2]\n",
        "      phisdot[j] = z[i+3]\n",
        "    # D = (1/omega)*((phis/theta0)**2 - 1)\n",
        "    D = ((phis/theta0)**2 - 1)\n",
        "    # 1 equation\n",
        "    dPHIdt = PHI_dot\n",
        "    # 1 equation\n",
        "    # dPHIdotdt = -1*(((Omega**2)*PHI)+(mu_s*PHI_dot)-(x0/((omega**2)*L))*np.sum((np.sin(phis)*phisdot**2) + np.cos(phis)*(np.sin(phis) + mu_m*phisdot*D)))/(1-((x0/(L*Omega**2))*np.sum((np.cos(phis))**2))) \n",
        "    dPHIdotdt = ((-Omega**2/omega**2)*PHI-mu_s*PHI_dot+np.sum( np.sin(phis)*phisdot**2 + np.cos(phis)*(np.sin(phis) + mu_m*phisdot*D)))/(1-beta*np.sum(np.cos(phis)**2))\n",
        "    # N equations\n",
        "    dphisdt = phisdot.copy()\n",
        "    # N equations\n",
        "    # dphisdotdt = -1*(np.sin(phis) + mu_m*phis*D +((omega/Omega)**2)*np.cos(phis)*dPHIdotdt)\n",
        "    dphisdotdt = -np.sin(phis) - mu_m*phisdot*D - beta*np.cos(phis)*dPHIdotdt\n",
        "    final = [dPHIdt,dPHIdotdt]\n",
        "    for i in range(len(dphisdotdt)):\n",
        "      final.append(dphisdt[i])\n",
        "      final.append(dphisdotdt[i])\n",
        "    final = np.array(final)\n",
        "    return final"
      ],
      "metadata": {
        "id": "wWFIwSVfwxyt"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# z0 = [0,0]\n",
        "# for i in range(N):\n",
        "#   z0.append(-1*2*theta0)\n",
        "#   z0.append(0)\n",
        "z0 = [0,0,2,2,0.5,0.5]\n",
        "t = np.linspace(0 ,1000, 10000)\n",
        "z0 = odeint(odes, z0, t)\n",
        "\n",
        "PHI = z0[:,0]\n",
        "PHI_dot = z0[:,1]\n",
        "\n",
        "phis = phis.tolist()\n",
        "phisdot = phisdot.tolist()\n",
        "\n",
        "for i in range(N):\n",
        "    phis[i] = z0[:,2*i+2]\n",
        "    phisdot[i] = z0[:,2*i+3]"
      ],
      "metadata": {
        "id": "71wJLxzFXLtd"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "last = 1000\n",
        "\n",
        "plt.plot(PHI[-last:],PHI_dot[-last:])\n",
        "plt.xlabel('PHI')\n",
        "plt.ylabel('PHI dot')\n",
        "plt.title('Swing Phase Space')\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "epmd7NF_aOxd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "outputId": "dfb20d70-3cda-4cc0-998d-a993650f24c1"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "last2 = 1000\n",
        "\n",
        "for i in range(N):\n",
        "  plt.plot(phis[i][-last2:],phisdot[i][-last2:])\n",
        "plt.xlabel('phi')\n",
        "plt.ylabel('phi dot')\n",
        "plt.title('Metronome Phase Space')\n",
        "# plt.xlim(-0.2,0.2)\n",
        "# plt.ylim(-0.15,0.15)\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "jkolOjye5gye",
        "outputId": "0ffba7a6-1f85-4ccd-83ac-9c4781c35c9c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "for i in range(N):\n",
        "  plt.plot(t,phis[i])\n",
        "plt.xlim(0,100)\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "16EIBe6jB9-y",
        "outputId": "7ba43c58-7321-40e1-d1f9-2207679b9df3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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KcuFIH8FPYB8dRVEUJT5pI/iJbqugKIqixCZtBL+xucPzvWwVRVEU96SF4AcClpPnOjzfy1ZRFEVxT1oI/unWTroDVkM6iqIoF5C0EPymFmdbBRV8RVGUC0VaCL6zrcJordJRFEW5YKSF4DvbKmhIR1EU5cKRFoLfs1OmCr6iKMoFIy0Ev+FsO8aoh68oinIhSQ/Bb25n1NBcsjLTojmKoijvStJCYevPtOv9ZxVFUS4waSH4Dc3tFKngK4qiXFDSQvDVw1cURbnwpFzwAwFLo3r4iqIoF5yUC/7Jcx10Bax6+IqiKBeYlAt+Q7AGv2jYoBS3RFEU5d1NygW//owIvnr4iqIoF5aUC37DWcfDV8FXFEW5kKRc8OvPqoevKIrSH6Rc8BvOtjM0J5OhuVmpboqiKMq7mpQLfv3ZNvXuFUVR+oGkCb4xJtMYs9kY86yX1zWcbdcKHUVRlH4gmR7+XcAury9qOKurbBVFUfqDpAi+MaYUeB/wK6+vVcFXFEXpH5KVKf1/wNeBYdFOMMbcCdwJUFhYSEVFBe3dlrPtXTQ3VFNR0ZCkplxcNDc3U1FRkepmpAXaFyG0L0JoXySPhAXfGPN+oN5au9EYUx7tPGvt/cD9ADNmzLDl5eUcbToHL61m2fyZlC8uS7QpFyUVFRWUl5enuhlpgfZFCO2LENoXySMZIZ3LgA8aYw4DjwFXG2MecvPC+rNtgNbgK4qi9AcJC7619lvW2lJr7UTg48Cr1to73Lw2tMpWq3QURVEuNCmtw9dVtoqiKP1HUpe3WmsrgAq35zecbSczw+jNyxVFUfqBFHv4bYwamkNmhkllMxRFUQYEKRX8hrPtFA3XcI6iKEp/kPIYviZsFUVR+oeUe/iFeerhK4qi9AcpE/xu5+blGtJRFEXpF1Im+CdaOghYLclUFEXpL1Im+M4qW721oaIoSv+QMsFv0EVXiqIo/UoKPXzdVkFRFKU/UQ9fURRlgJBSwR82KItB2ZmpaoKiKMqAIqWCr969oihK/5HSKh2t0FEURek/Uuzha8JWURSlv0hplY56+IqiKP1HSgTfWjjX0a0xfEVRlH4kJYLfZeW3eviKoij9R0oEvzso+OrhK4qi9B+pEfyAKL6uslUURek/1MNXFEUZIKTIw4esDEPB4OxUvL2iKMqAJGUe/qi8HDL05uWKoij9RuoEf6iGcxRFUfqTFAm+ZbTG7xVFUfqVlAh+IACj83JS8daKoigDlpSFdArz1MNXFEXpT1KztQIwWgVfURSlX0nZ5mmjNKSjKIrSr6RM8NXDVxRF6V9U8BVFUQYIqRP8YRrSURRF6U9SJvgjh6jgK4qi9CcJC74xpswYs9oYs9MYs8MYc1fcNzWQlZmysUZRFGVAkpUEG13AV6y1m4wxw4CNxpiXrLU7o70gU7fQURRF6XcSdrOttbXW2k3Bv88Cu4CSWK9RwVcURel/jLU2ecaMmQi8Dsyx1p7p9dydwJ0Aw4tKFz3z+98l7X0vZpqbm8nLy0t1M9IC7YsQ2hchtC9CrFy5cqO1drHf1ydN8I0xecBrwPettU/HOnfGjBl2z549SXnfi52KigrKy8tT3Yy0QPsihPZFCO2LEMaYhAQ/KZlTY0w28BTwcDyxVxRFUVJDMqp0DPAAsMta+5PEm6QoiqJcCJLh4V8G/BVwtTFmS/DnpiTYVRRFUZJIwmWZ1to3Aa27URRFSXN09ZOiKMoAQQVfURRlgKCCryiKMkBQwVcURRkgqOAriqIMEFTwFUVRBggq+IqiKAMEFXxFUZQBggq+oijKAEEFX1EUZYCggq8oijJAUMFXFEVJJq0nob05+XabDiRsQgVfUZSBx64/w8vfgbPHk2t37yq4Zzr8ZBZUb0ye3dZT8KtrEzajgq8oSmLU74a9L0KgO7l2N/0O7i5l7rbvQWdr8uzufxl+fwe8+RN45Dbo7kqO3Y4W+NPfw4iJkDMEnv0yBALJsb3pQWg9kbAZFXxFSTfaTkMS7zUNwMnD8PSd8NqPkivMx96BX1wOj3wM/vSl5Nlt2CuCOXwso05sgDX/lRy71sKL/wSjpsKHfgm1W2D7E8mxveOP0FwH7/9PuPpfoHYrHHkrcbvWwubfQdmyhE2p4CvvbqxNngcXzt5VsPpuOFObPJuBADzxafjBeGbv+GHyvMPONnj0dtj+JKz+Pqz5WXLsWtsjyiz8a9jyEFRtSI7tdfdBRiZ8+jkaRq+At36WHC+/agM07IbL7oJ5t4nwb3owcbsAWx8VexMug9kfgpw82Pb7xO027YfGvTD3owmbUsFXUk8gAFseYWzNquSK88kj8LMF8MMJsOMPybO7dxU88lF47Yfw2w+IoCaDTb+Vdk4up7DxbdjwQHLsbn8C6nfCxx+GGe+D1++RWUSiHH4D6irhqm/A9XfDoHxY98vE7Xa1w7bHYfaHIa+Q6pKboOMs7HkucduVT0HWIJh1CxgD82+Ho2sSH7jbzsDRt2HmB8RuzhCYfoOEuhKdre1/RX5P1Ri+Eo3qTXD4reSGBhr3wy+vgl9cAXU7k2f31e/CH7/AjL33wnNfTY5Na+Gpz0rFxIhJEm44W5e43UA3vPBNKJwJtz0MTfvgnfuTYDcgnnfpEvirP3Iqf5aEMZIRfln/KyiaLQJ0xVego1nCD4lS+ZR4sXNuhdw88Wp3Pyux7EQ4/Ia0cfaHADhVMBvyiiXRmigHXhEPfNBweTz9+uDxVxOze+h1CHSdL8pTVkJLPdTvStz2iIkwclJidlDBd0/9btj6mIzkyaLtDLN2/Eiy70fXJs/uhl/D/6yE39wkU/hk0N0Jj90Op47AmRoJPXS1J2636QC89VNYcAfHSm+Gjb+Gmi2J2z1YAVXr4drvwEd/IwKy7r7E7e5/GU4cgKu+DjPfL+Kx4X8TD78ceQtOHISld4IxVJe8T/r60GuJ2T11VOLU828Tz7NkIYyeDpVPJmY3EIA9z8PUayB7kBybdQt0noPDbyZme99LkDUYJl0hj00mTLkaDr6WWD+frpLQyNRrQseK58hgkqjgH30bMnOhdGno2KSr5Hcin6G1UL0hKfF7SKXgt56S6d+h15NnMxCAVf8MP5wEz30teTHQI2/D/VfBHz4vItp+Njl2n/kihQ1vy4X46O3J8UDP1MAL34LJK2Hux+D1H8Px7Ynb3f6EfFlu/m+45b+hcU9ykl1r74OMbLjmXzk88TbIzYe3703c7uaHYPAIWPAJGD0Vpl0PWx5JPGRU+TQMKpCpO8DCT8HJQzK4JMKe50QwZtwEQNOoJSJ6e55P0G7w9Ze8X34bI57+kbcTqxVv3CMJymnXhY6NXyHhkgOr/dsFOLIGypZC9uDQsckrpUrl+Db/do+tk98T3hM6ZgyMXw5V7/i3C5IbGDsfsnJCxwrKYNi4xMozz1RLP5csSqx9QVIi+MYG4Nc3wfNflxjo1seSY/id+2UaPHJS8O+fJm6zu0tKrYaPg5vvFfF8KwlJr2PrYdefOTTpdvjUMxJTTUYybd0vobtDKgVu+jHkDBMPOlHWPyBhjBk3ype8aBa88z+J2ezukpj1jBthWDHdWUNhzodg91+g45x/u52tInQzPwhZuXJs/m3yxUnki93dKXZn3ASZ2XJs+vXige570b9dgL0vwKQrJTQCBDJzYXK5HE+Ew29AwQQYNSV0bOq1EOiU5/xyZI38DhfP7EEi+ok4ce3Nkhfo7dFOWCG/ExlYqzbKgFQ85/zjpUtkJtRc789ud6fMokoX931u3KVQs9mfXQgNFhez4Od0nIT6HfCxB2VK/NzX4VyCNabtzVDx7+IJfO4V+VK+8ROJ4SbCrmckS/7e78Kld0hcce1/Jx6nfOd+GJRPdckHoHAGzPkwbPxNYna7u6RSYNp1MugNLoAFt0vsM5FQ1MnDMq10wgLGiOdcu0We88vRNXCuEeZ8JHRs9oehs0Virb7trhUbjlcLMOUayMhKTEBrt0L7aZj23tCxwSNE5Pat8m/3TI2Ec6asPP/4lKtFiE4d82fXWvHkw0UZREwzsiUM4ZejayUUMqJXXLlsmSSI/c6CqzeCDfQV/PwyGFqUmLdcvVG8cGewdigJCrXfCqO6HdDVFlmUSy4V/Wg95c929Ub5rMbM9ff6XqRE8LM7T8sXe9bNcNM98iVa/6vEjO54GtpOQfk3RZCu+jq0n5FStETY/JBcbMGpNks/L/Hgnc/4t9neLMmt2R+mOys4bV34KbGbiHBUrRcvdv5toWNzbpWLMZHQwJ6gSM66JXTMEdNdz/q3e7BCvOPJ5aFj41dA9lCJ1/rl0Osi7o5XCJKkG78isVitE5ueePn5xyddCccr/Ve+OMI7fsX5x8cvDz7vM7/TtF8G1N52swfB2HmJlVAeXSvtM+b846WLAes/D3PsnTA7YRgjgupX8B0vvCSCFz52vlyH1T77w2lTRA9/ofyu9dkfx7dD0czQTDVBUhfSWfJZeVA8S5Ibm36XWMx9y6MwekbIMxh3qYyKWx7xb/PcCRGleR+TmmCQi7xgQmJVDgcrJLk158OhYxMuEw8mkYFk3yoRuilXh46VLoGhhZJs9MvBChg5+fwqgZGTJPl3sCIBu6/Jl9ipmACJgU54T2KJrkOvi93cYecfn3CZeGN+hfnwm3KN5RWdf3z8MsBKmM4PR9fKIDdm3vnHi2dLSM6vJx4p7OJQulQqubo7vds9Wwenj0ZOJDperl/xrNkMo6bJ7DSS7ca9/rzl+l1BL3xh3+dyhogO+Q29NOyWaqWCCX2fG3ep/PY7ADbshcJL/L02AikR/EBGtnz5HBZ8Ui6gmk3+DJ47AcfWyowh3OOY/SGx6Xe/jAOvyvTS8e4hlPQ69Lr/hSD7X5Yvctny0LGMTAkVHKzwX4q3/yWxOSg/zG6GDKgHK/yVaHZ3itBNLu/73MQrRIz8iEbrKflsItmddKV8sc/UeLfbdka+uJOu7Pvc+OXyefqJAwe6RZgnXtb3uZLF4iEe8+mJH30bypZAZtb5xzMyJXnpV/BrNsu1MGpq3+fKlkBXqwyAXqmrlN+9ByiAISMlzON39lC/Uwa6SJQExdOPt+yURvaO3zsUz/FfPlm/S8KyvWc7IP0xbKw/2+1n4UwVFE73164IpETwO3JGnt85094rXxi/Cyv2rQoK8w3nH592feh5P+x9EYaMCo3SPXavky+Ln/Iza2UhxaQrz8/og4hf60l/lQjNDTL9Cy85c+ipB/ZRO1+9SRa9TC7v+9zEyyUMVbvVu92q9fKZOaV34Thi7XioXqjdArb7/MHUoTQozH5CJI37pB9Kl/R9LjdPQiR+7Ha2ypqGSHZBBL9+l7+KmrpKKJ4bWYic9/PjiTuDRFRhXujvmuhokZxQ0azIzxcH49h+xLNhl8TCw5PX4RTNgrO1/nKJDXukoCEahZfI+3ulcW/o9UkiJYLfmd1rqj1kpEw79/hMqO19QRJIY3sJc/FsGF4qwu2VQEASh1OvDYVzHCZeLiVz+17ybrfpgMxmpl7d97nJ5fLbT1mb47VGmr47dv3ExXtK2SJ4thODYu2nKqN6E2D6DqYg3lbWYH/xWmfqPG5B3+dyh0mYz48wOwI2NoJdEAGt2ew9LFm/UwaoSN4yBI9b7554ICADSTRRzi8T7/94pTe7IG0eNla+t5Eong2nj3kPnTXsBqzErCORVyQOmJ9ZSf1umen0Ttg6OIOM18Hk3AlxpgpnRD+naKaEZrxeGw1BwR8dw7ZH0mfh1fTrpXLndLW311kbCjlk9Pp3jBGP99Ab3sMkTfvgXFNI1MLJHhScavvwQJ1p/4TL+z6XVyQXnp9yuar1Er8fO7/vc/ml8gX3U5JYvVFik0NHR2hvoXyJ/EzfazZJDqB3nB0ktDF2vj/Br90ig3yk9kLQ+9zmPbxVu1VK+kZHmV6PnS+znRMHvdl11khEq8IYGxwIvM76Th6SSqUxUUIYxojHXOdD8Osqow8kEAqbeF2N7ZwfzbYx8v3wM1Nt2AVFMTzlYkfwPdpu2C2/Y3nhhZdIRODUYe+2M7KTssLWIX0Ev2ca73F3uaYD0NLQtxLBYcJlUgXk9YN0vMDxEUIDIO/nJwF47B3xrKIJR9kyqRf26g1UrRfRCF+sEgB8rUwAAB7vSURBVE7pYn9JxepNsWuASxZJWMCLgFobtBshgRZut3ab9/xAzZbI3r3D2PlyPXgtJ63dKkLWO87u4Hjoxz2GMo5vh9zhkRN+AMNLYPBI7yESZyCJFrMGGQzqdnq71ro7JYQRU/CDz9V79MTrd8nMbsTE2Lbrd3trsxMqihV2GTZWvpd+BT/WYOLMWOp3e7PduFdCUNFmJT5IH8EvniMd7tW7PRqjEgFCpXle48HH1sn0MVLCy7FrA95FtGq9JPl6z0YcypaKIDnxOzcEukVAo8WBQaoyzlR5S4Q2N0j4KZbgj1sopaBe7J6plmnwuFiCv1C8Ii9T7LbTsu1BtLALhGZAXgQ0EBAPO9LsyaHwEsjM8SfMxXOiXw/GiJfvdbV0XSWYjOjhEZD37WyR2YBbmvbLwr5YA8nwEvkuew291O+Q0EjvEGo4RbOkzaeOuLfbsCf42hh9YYzsN+R1VtKwRyqshpdGP8cJ93iN4zfsiR0q8kH6CH5GJox/j2z45YUja0SYo3nMBeMlnOFV8I+uFW87UsILQpUZXioo2k6LgJUtjX6OI9peKknqd8mXIKbgO3Y9hF+cqql4Hn74uW6oduzGEXzwFtZxRDGWMBfNktCXF2E+eUjWdMSym5UjguJ5IKmMv6hmzDzxPL3Mdo5XSnljtBkfhMI9XgaTeAlbCBNPHx5+tIStQ5GP0EuPFx5D8J3n63d5m6027JYqmmgDNsjgN7zEm4ff2SbXXRLj95BOgg9S8nbigLetSo+skfBKNGEGef7IGvcfZEujtCOWMPupzKjeCNjYwjxqquzV4iXe7gwOkRZ+OIydJx6ol4GkeqN4iWOjJBRBxCojy5sw12yS18TyEkdMklWsnuzGSNg6ZOV6F+aehG0MwXee95If6ImzxxH8sfPFq3Y8VTfUVUaP3zsUzhSnxZPgV8pnN2pa7POKg96y6+9ck8wUi+MJfjB04sUTr98l137vVcF9bM+U2bWX2Wr97tihIgevlTonDkgEIR09fGPMDcaYPcaY/caYb/o25FSCuI3jn6mRqV20cE6P3fdICMFtQs2pTIlU2hfO+BUSv+7qcGl3PWBiC7MxMiB48cSrNsgsJ9YFnZUrnqJXwS+aBTlDo5+THdybpNqjh188O7TLYiSMkZCPlwUrtVtks6reC6N6M3a+iLhbMardKsmzeB7i2PmywdfpKnd2nURsXA8/+LxbYW49KVUysQZUkP4fPc1b4rZuh3idvUuKe1M8W8pYTx11Z9fx2OP1ce4wyXd49fBHT4+ef3Fw3rvBpSfeehKaj7sT5aKZUtrrtnikJxmcZoJvjMkE7gVuBGYBtxtj4gzTURgzT1asuQ2/OOdFS9g69CxRdxl+ObpWPIJIJYPhlC2T1Xtuv4hV78hIH74wKqLdYO212/1vqtbLIBFrlgMy0NRscbdjpLUi+LHCLg4lC92XJAYCwcSqC7vjFohX5HaBW7yErcPYBbLlgFtPrnaru+XtY4IzALcVNce3i7ccr8561FRJZroVZsf7dbP/SvEcb95yrFLP8+w6iVuXtnsE34XtopnuRRmCC6Nc1LIXehT8Bg918oUzRCvcDoANewETPYfok2R4+EuB/dbag9baDuAx4GZfljKzRERdC/PbMkBEq2F2GD1DRNZt+OXYOhGFWB4ohJaWOzOCWASCKzzLYoRzHJz9SNyEM1pPyVa1sWYNDiWLg4lQF1/Ck4fEg3GzS9+4hRLjPnEg/rknDsq02c1AMu5SuamEm1hw+1lJKMZK2Dp4SdxaK+fFC+eAiJzJkLCOG45vl2sz3nWWkSki53YgcQaGeB4+BGvmj7rbrqD1pCT+3Qi+I4Ju4/j1OyWUOWxM/HMdb9lNTqP9rMx2YlXROAwdBUNGuy8UcEI0bmw7/eE2LNewW6qVYuVgfBBnjuOKEiB8O78qoM8mG8aYO4E7AQoLC6moqIhobHxgDJPrX+HNl/5MV+8FWr1YvPMlOoZOZdsb8Ve8zh0yjUF7VrM+yvs6ZHR3cHnVRqpK38/BOOcCLM8t4symZ9nZHntSM6TlGEvbTrO7JZ/jYXabm5v79EVmVyuXYzj8xuMcORbbax9xYjPzgS1NOZyK095BrV0sB/asfpTacbFXFBbVvc4sYH2tpSWO3aHN3SwBdr38EHVjVsY8t6juNbFb003LmfPt9u6L3LY2VgB7X3ucmpLYK03zT+3gUizbmjI5EfczbuMKMjjy9h85fHxIzHNz2xpY0XqCvc2DqXFxPSwZPI7WylepNHFmncCKIxs4OWIeuyPY7d0X0+0oCo+t5a3Vq+PO5GbsXsWo7OGs2bgbTGyBGdkUYB6w+cWHOV0QW8ilj2FbXSBuH4N8N05XVrArEN8ZuXTf29jcEra81ndxYO++KG6EmYFO3nnhUc4NHR/T7rAze1gEbK8P0OSizfNzxpBx4B02uzh3yv6XGZeRwxtbDoI5HPPcrM5mLgcOrHuOY7VxBnhg8ZHNtA0qotJFOzxhrU3oB7gV+FXY478Cfh7rNdOnT7dROfSmtd8ebu3u56KfY621505Y++18ayt+GPs8h9fvEbstTbHPO7JWztv5Z3d2n/ystffMsDYQiH3exgfFbv3u8w6vXr068vn3Lrf2dx+J//6rfyD90Ho6/rmBgLU/mGjtH78Y/9znv2nt94qt7eqMf253l7X/Ntbav3zNhd1vRbXbpy8CAWt/ONnaP7ho75qfS/+eOR7/XGut/flSax/6aPzzdj0rdo+uc2f3ib+x9j9mxT/vbL3Yfeu/Ij7dpy/W/lLOP10d3/Yvr7L2Nx+If5611p6qErvr7o9/rpc2WGvtwx+z9ufL4p8XCFj7/RJrn/3/Ij7dpy9qtko7tj8V37bzvWvcH/9ca6199ivW3l0a//tsrbUP3mLtL65wZ9da0Ymn/zb+eV2d1n53tLWr/qXPU8AGm4BeJyOkUw2UhT0uDR7zR8kiiZ/Hi+Mfewew8eP3Dk4CNl74xQknub2lWNky2YPjdJw9y6uCC67iVTc4lC6REFC8uHjV+mBeYHjs8yBsi1kXCVbnDj7xEl0gIYex892VZtZsDlYMubBrjPsbSNRskcUzw4rjnwsS+nGzCVftVgnTuAljgPxvZ6ri78nSk7B1EXYJPy/eVgjdXRKScLt/+vBxUg3lJj9QVynnDhvrznbRLFmxHq+o4XSVJHjjlWQ6jJ4un4mbWHv9LlkhHWsxVziFMyQ86Sa/47ZCJ9y2mzafPCxVWUkuyYTkxPDXA9OMMZOMMTnAx4E/+baWPUhiwvHi+EfWSOWE2zvBlCwM3vQhThz/2DpJlOQVurPrlG4ei1NGeXRd8MYTLru8bKns79+0L/o5XvICDiWLgptxxbhBRVeHCJ2bvECP3YXxV8YGusVuvGR4OOMWyJck3h2ware4i7OH222ui7+Tau02GaRjVSqF4+ST4uUHegQ/Tv7JwRlw4sXxTxyQ5KCb+D0Et1iY4y7WXrdDzo1XHOBQPFtyMLGuYQhL2LoU/OxBsl23m1xUw674i7nC6anUiRPHbzsNZ2u87WRZeInE8ONVhzUGw3BJrtCBJAi+tbYL+HvgRWAX8Li11sfuRmFMWCFeXawv+dG18qXNiR2D7SF7sAhCLA8/EAjd2MEtRbNlpV0su+dOyIfo5UbEpS4GkqZ9Mih4suviBhX1O6C73dtt1cZdKq+JJRyNe6Xu3JPgXyqbi8XyQNvOSBLPTeWPg5PcjVf26TZh22PXqdSJU7lVuw3yx0ffgKw3g/KlHDGeJ+4kjGOtneiNUzMfazYZ6A5uXexyIIGQgMerAupJMnso7iu8xN1CJjeLuc6z6wh+nORqz+pdL7ZnyPUfr2zXSRqno+ADWGufs9ZOt9ZOsdZ+P2GD498jnkG0rVs72yR84Dac02N3uYQzutojP9+0T+qo49Xfh5OZFdynJobgO7XvXoTZzQKsnvUCHuw6ohhrW1xnDYAnD9/FilsnNONV8CG2MNduAay7yh+HMXMBEzus09wgXpwX8RwyUpbZx/PEj2/zZhekzfFCOse3ys3Qo608j0Tx7OB2BYejn3PioNy0x20ICuQazsiKv6dO3Q4Z/OKVK4dTNFNmM51t0c9pPSnh1ni1/eG4rdRxu24gHCdE0+hiMBleGnljwQRJr5W2DmVLASP344xEzSaJcXkV/LJl4oVGm25Hu9WcG7vHK6PvWX5snaxo9OIxZ2RIHD/WXj3H1klM1Uut7tDgAq1YJZ/VG+XuW/ll0c/pzYiJsslXrPxAzWYpo3WbxwCJFw8tih3Hd97Ti4efmyeiGGsgOe5yhW1vxs6LXZrplJC6Dec4FM8RkYs1863dJiLkZcMtJ1wUa3bmZjO23mTlSB/H9fB3uM+ROBTNlJWoscJFzgzAixfu2I4Xa6/fJTP7/NhVQufhtjQz3s6eCZCegj+4QC6saBupHXwNMN5CLxA6P1pC+MgaGd2j3SQhGmXLJOwQTUSPrhMRcBt+6rG7VC68aDXSx9ZL6MdtTNWhZJHsyBmNqg1yjhe7bhKsNZsllOI2j+Ha7ibZM2noKPd2QUKCsTx8R7S93kB6zDwRomjC7HjpXgeSMXNE5KJ5n9b6mzkUzpQkaKzZQ12lOC1eb8YRbzvjrnYJx3kVfCf0EssTd97Xa5vdxNrrd4ooe7mWndlDrMEk0C39kcSbnoSTnoIPcoOQo29HXm26/yXxft3GPx3yiuRCiXQj60BAbjwyudy7gJYuBkzksE7HOQnpRLqBSFy7S5AFWBHCLz15AQ8J2x67iyVUEeneAy2NIlZewjkOJQvli9DR0ve5zlaZWXkJuziMWyD/ayS7ANWbvXn3DmMXyJT/bF3k52u3ykAyeIQ3u2PmijBH85iP+4izQ8i7jhYuOl0lYQyvM4ecITBySuz8wPFK8dbjLRLrTfGs2DdDadgjzpJXwe8JF8US/F1yK9H8GDtZRsJNpY7XCp0e25fE9vBPHpak+4AT/Ok3SBz/YK+7P7U0yhR+2nv92Z12rXjyvcMvddtlv52p13q3ObhAvK9IN/Q+8paEkcJvLO6W0iVSWRTpTlVOv0y6yrtdZ++hSDMo55gfuyWLROgieeNVGyQM52fgG3ep2I0UJunZwtnnQAKRQ3zWygAea6O7aPTctCRK6LBmi9xY3m15o0PBBNk7P1pC2M1uodEojrO7pZvN2CLhbJUQTZh7dt/0aDsrR0Q/nuAXzfTuwMWr1GlpFK3wEr93cEozo80e3O7s6ZP0FfzSpZK07H3bw32rAOtPmEHuRxvohEO9RHT/y/LbjzCDDFBH1/atv97/itQBx9vgLRK5eRKG2v9K3+f2vypJLj+ebfFcibdHGqAOviZekZfEqsP4FRIaiHTLwyNv4SsMB7IlBEQu1XU22vOSaHcYM0/CFJES46eOivfvNZ8DkvsYMip62OzYWn+huIwMGaSiJdxrt3hbMxBO8RzZTiPSjLqlSe5h4FWUISRc0QaTukr5foyc7M92tHCRtcE7c/nY1itepY4zyPgS/EtkttMcZVbp2PaSdPdA+gp+ZhbMuAl2P3t+LHTb4+LpuNkzJRJlyyE3H3b9+fzjO58RkXO7cKc302+QqWm4OFsrA9SEy/zviTHtvX1v/Wit3G93crm7BUy9yciAyVeJ4Pf2NA69LttU+7E7uEAGoEgDyeE3JdQxuMC73bxCiQX3HqRB2puT58/Dz80TAY10M3onPOdngDJGBopIt8A8WycVL37sQuwCgaNrRZTdrhkIJ9b9B9xsvx2NgvHiuEXLldRsls/Wz/VWPEd2y420yO3kISlZ9uO4xKvU8VOh49BzM5QocfyG3VKh42YhpQ/SV/ABFnxCYmk7npbHJw7Kl37ebd6SJeFk5cDsm2Hnn0JfmvrdMq2f+zH/bR23UG6kvvOPoWM1m6WqYpa/veQAmBoMXe19/ny7Z2tDz/lh8kqxER63bdwv7Z0cez+c2HbLJXwT7im2N8t6Auc2ln6YdJUIWu+S2sNvyOzJ723gJl4h7e2dHzj6toRPvFZ4OEy4TOKxvfMkzj2NExH8SAUC3Z0izH5mJBCWh4ow23GqzPzMJk1wO/BI2313d0l4NtZ9J2LhDECRQoh+KrfCGTMneq6kZrN8172G5CAUm4+2hqB2q/fcjgfSW/AnXCZe4es/Fi9/9b9LTHvJZxOze+mnpO5442/k8dv/JdPKuR/1bzMjQwaiPc+HbuCy6beyTcSsD/q3WzRTRGfrY6Fj234vtdYzP+Df7oyb5Eu84w+hY85glYjdKVcHZzovh44deEXyGNNv8G930pWSzApPjJ+ulsVckW4079ruFRLiC1+Bba0k9sevcL9CszdOCK93RdjRtXKt+YmzQyin0FuYj2+TOnm/A8mgfLnOIhUeVK33V2XmUOps990rcVtXKbu3+smTQMh7j1QKXLNZ+tlvLLxkkYShIlVaVW/0XsXmkFckg0WkQapnAaGPWYlL0lvwMzLgvd+Dk0fgvhWw/XG47C53W6jGomyJeKKv/QjW/gK2PAKLPu1+O4VoLP6MXAQVd8vN1bc8Apfe4b3KIxxjxEbVeinvPHcCNj8MM9/vLzzikFcofbD1MdlKIdANmx8Skcsv8W93/HLIGwOVT4WOVT4tOQO/3ieIMGcNkpmZw67g34kMJGXLZfDc91LoWOM+8c6nX+ff7pi5EjrsXXSw7yXph3h760djcIEkQnuHt9zeGyIWZUuD+zeF3aSju1MEzsvivj52nWqzXrOSnlCRT8EflC+x7khhqJrN8hn4nfmVLJaikd4J/bbg/ab9zhx69rOKMOM5vg2wA1jwAaashFvuk1Vny/8Oyv3fUOs8PvAzCe+88A2ZZl39z4nbHDkZlv0tbHoQfnmlxJav+Gridhd9WhYf/flL8Ie/hY7m5Nhd/gVJxm36rcwaTh6S9idCRibMvRX2viAD9ZlaycMs+IS/OK1D7jCYfr3MSLraxQvf9rjEcb3sZ9LHbh5MvUZyOM7WAs5MZ9r1/u1mZMqAsef50A1nmg5IyeuMG/3bBak0O7r2/LDZ3hflOh7uI8zgMOEyCaGGL0Y79o7MHPwUHTiUBMNFvfexOrZOrusCD4uX+theJANHeC6qq128/hIfOQcHJ1zUW5idvvGTM3IoWSQL71pP9rId9Pr95iddkP6CD7DgdvjbN+GGu/1PsXszYgJ8cR3c8RR87uXkLWN+73fhyq9LmOGOJxPzlh1yhsJH/ke8zn0vwnX/5q/6oDdTr5XY+Avfgj//o3i7iYRzHJZ/UapFnvsq/OUr8veSzyVud9Gn5U5Vmx+SZG3NJjmWKHM+IusS9r8k4rz5d9IvBR5WGkdi5gdkqw7Hy9/6KGAknJYI066XMNS+VfL43Anx8BO1O/Ua+az2hlXG7Vsl9e6J5HUGDReRCy9oCAQkbDa53F9oxGHCZXJNhFfrVG2QUFEiOaO8IllF2/uWoMfWASYxL7xnMOkViqreKBVeiUYaYnBxCP6FYugoET0/VQ3RyMiEq/8JPvGYt60U4jG5HP6xEu7aCu/5++TYNAY++hvJXcy6GT722+QMqPklcN33RSz2/EVmTyPj3EDaDZNXSshi1T/Dk5+RL+SldyRud9bN8kV75buSLzp1FJZ9PnG702+UeO2a/5LtFDY9KNdbogPJ+BXyv2/+nTze8ojkTeZ8ODG7Q0ZK6GbnH8VjDgRk5jPhssSrRqa9VwStpVEe12yCc01SJp0IU4IDUfhiyoOrZeBKZFYCMPFycSzCQ1wHVkv+xeuiz3DGLZT29c4bHXoj8TbHYWAL/sVGXqH7fb3dMmQkfOg+mUEkmhsJZ9md8NmX4W9WSd4lGTgD1NgFcrPy2x9Nzi3gMrPhfT+RJN1rP5CcQKLeMkjI8PIvS7z9/nJoroervp643YwMWPTXUv5a+TS8/XMZBLxuARGJBZ+UGPXhN0U4Tx5KzqA68wOAhe1PyOOtj0nuZJrP9TQO+aWSbN71rDy2VvI849+TWI4LZMbTejKUI2g7I2s2piQw24HQjCd8kKrfKTMVPwsePZCMWxwqSmT8bPsQj2Fj4G+ej3+eV6ZfB599KVhGe0tiYYZwln5eKlT2vgDX3+2/BLE3K/4OtjwsM52MbBn8ksGcj8Dq70soLtAlNeEzE6gycyieLSL3zv0i/tsel+q1RAoaHObeKrOzpgPBpOoecTgSZcrV0rc7/iCf285npE+S4QxMvRYqfiArxfMKYc9zcnxyeeK2Y6AevqI4lC2B+R/3vl9MLDIy4IM/g6/uhRVfTJ7d7MHw6b/ANf8qv5NV2ZEzBG7+ueSLztTALfcmrz9W/l9ZS3PvcomxX/m15Nid/wnIGgyr/gVe+Y4s9EqkxNphyEi45H2Se2k7DRv+V/Yc8ltVFM7MDwJWiiWshW1PyKwkGTm/GKiHrygXK8PHwRVfSb7dqdfCV3bLLCcZHni43ev/XTzm5V9I3g0+ho+FK78Kr35PHt/4Y29768fiPV8Sz/7+chmsbr43ObO/4lmyPmHdL6SPG/eI7QuMCr6iKH1JJCkZixVfTO5Mx+GKr0jYKDNHYu/JonQRvPc78NqPJb8x/xPJs33dv8H/Xg/PfFHWVsz7ePJsR0EFX1GUix9jEl/fEI3L7kpe4UE445fBJ5+UbTyWfC6xdSouUcFXFEVJFdOuTbxSyQOatFUURRkgqOAriqIMEFTwFUVRBggq+IqiKAMEFXxFUZQBggq+oijKAEEFX1EUZYCggq8oijJAUMFXFEUZIKjgK4qiDBBU8BVFUQYIKviKoigDBBV8RVGUAUJCgm+M+bExZrcxZpsx5g/GmARvIqkoiqJcKBL18F8C5lhr5wF7gW8l3iRFURTlQpCQ4FtrV1lru4IP1wKliTdJURRFuRAYa21yDBnzZ+D31tqHojx/J3AnQGFh4aLHH388Ke97sdPc3ExeXl6qm5EWaF+E0L4IoX0RYuXKlRuttYv9vj6u4BtjXgbGRHjqn6y1zwTP+SdgMfBh62IEmTFjht2zZ4+P5r77qKiooLy8PNXNSAu0L0JoX4TQvghhjElI8OPe4tBaG/P+W8aYTwPvB65xI/aKoihKakjonrbGmBuArwNXWWvPJadJiqIoyoUg0SqdnwPDgJeMMVuMMb9IQpsURVGUC0BCHr61dmqyGqIoiqJcWHSlraIoygBBBV9RFGWAkLQ6fE9vasxZQOsyhdFAY6obkSZoX4TQvgihfRFihrV2mN8XJxTDT4A9idSSvpswxmzQvhC0L0JoX4TQvghhjNmQyOs1pKMoijJAUMFXFEUZIKRK8O9P0fumI9oXIbQvQmhfhNC+CJFQX6QkaasoiqL0PxrSURRFGSCo4CuKogwQ+lXwjTE3GGP2GGP2G2O+2Z/vnWqMMWXGmNXGmJ3GmB3GmLuCx0caY14yxuwL/h6R6rb2F8aYTGPMZmPMs8HHk4wx64LXx++NMTmpbmN/YIwpMMY8Gbxd6C5jzIqBel0YY74c/H5UGmMeNcYMGijXhTHmf40x9caYyrBjEa8DI/ws2CfbjDEL3bxHvwm+MSYTuBe4EZgF3G6MmdVf758GdAFfsdbOApYDfxf8/78JvGKtnQa8Enw8ULgL2BX2+IfAfwb3aDoJfDYlrep/fgq8YK29BJiP9MmAuy6MMSXAl4DF1to5QCbwcQbOdfEb4IZex6JdBzcC04I/dwL3uXmD/vTwlwL7rbUHrbUdwGPAzf34/inFWltrrd0U/Pss8qUuQfrgt8HTfgvckpoW9i/GmFLgfcCvgo8NcDXwZPCUAdEXxph84ErgAQBrbYe19hQD9LpAFoMONsZkAUOAWgbIdWGtfR040etwtOvgZuBBK6wFCowxY+O9R38KfglwLOxxVfDYgMMYMxG4FFgHFFtra4NPHQeKU9Ss/ub/IfdSCAQfjwJOhd0jeaBcH5OABuDXwfDWr4wxQxmA14W1thq4BziKCP1pYCMD87pwiHYd+NJTTdr2M8aYPOAp4B+ttWfCnwveMexdXydrjHk/UG+t3ZjqtqQBWcBC4D5r7aVAC73CNwPouhiBeK6TgHHAUPqGOAYsybgO+lPwq4GysMelwWMDBmNMNiL2D1trnw4ernOmYsHf9alqXz9yGfBBY8xhJLR3NRLHLghO5WHgXB9VQJW1dl3w8ZPIADAQr4trgUPW2gZrbSfwNHKtDMTrwiHadeBLT/tT8NcD04IZ9xwkGfOnfnz/lBKMUT8A7LLW/iTsqT8Bfx38+6+BZ/q7bf2NtfZb1tpSa+1E5Dp41Vr7SWA1cGvwtIHSF8eBY8aYGcFD1wA7GYDXBRLKWW6MGRL8vjh9MeCuizCiXQd/Aj4VrNZZDpwOC/1Ex1rbbz/ATcBe4ADwT/353qn+AS5HpmPbgC3Bn5uQ2PUrwD7gZWBkqtvaz/1SDjwb/Hsy8A6wH3gCyE11+/qpDxYAG4LXxh+BEQP1ugC+A+wGKoHfAbkD5boAHkVyF53IzO+z0a4DwCBVjweA7UhlU9z30K0VFEVRBgiatFUURRkgqOAriqIMEFTwFUVRBggq+IqiKAMEFXxFUZQBggq+oijKAEEFX1EUZYDw/wNmO+ZRmnmPHwAAAABJRU5ErkJggg==\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "data = []\n",
        "for i in range(N):\n",
        "  data.append({'Frequency of the Metronome':find_freq(phis[i]),'Amplitude of the Metronome':Amplitude(phis[i])})\n",
        "df = pd.DataFrame(data, index=[i+1 for i in range(N)])\n",
        "df"
      ],
      "metadata": {
        "id": "SvvFGlBFCFum",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 112
        },
        "outputId": "4f2c5579-2a05-4fed-d0eb-73de803cc830"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   Frequency of the Metronome  Amplitude of the Metronome\n",
              "1                    0.263132                    0.055392\n",
              "2                    0.303000                    1.877504"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-a52952eb-bcbc-46bc-a69d-b5ec8c8925df\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Frequency of the Metronome</th>\n",
              "      <th>Amplitude of the Metronome</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.263132</td>\n",
              "      <td>0.055392</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.303000</td>\n",
              "      <td>1.877504</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-a52952eb-bcbc-46bc-a69d-b5ec8c8925df')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-a52952eb-bcbc-46bc-a69d-b5ec8c8925df button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-a52952eb-bcbc-46bc-a69d-b5ec8c8925df');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 280
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "(-11 - np.sqrt(121 + 20*852))/10"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "o314QYxBb9Hu",
        "outputId": "58b18690-8aec-4eae-b8b9-46e19a239edb"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-14.2"
            ]
          },
          "metadata": {},
          "execution_count": 282
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "BF29VqtOcGLg"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}