Motion Simulator v3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9cd27894",
   "metadata": {},
   "source": [
    "# Motion Simulator version 3.0\n",
    "\n",
    "**Ver 1:**\n",
    "\n",
    "- Implement the input section (see plan on OneNote)\n",
    "- Implement the Processing (see plan on OneNote)\n",
    "- Output: print out the array of points \n",
    "\n",
    "**Ver 2:**\n",
    "\n",
    "- Improve output by plotting the trajectory\n",
    "- Add 2D and 3D plot options\n",
    "\n",
    "**Ver 3:**\n",
    "\n",
    "- Animate the trajectory\n",
    "- make simulated time agree with the animated time "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c3d9736a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import libraries\n",
    "\n",
    "# Numerical Python - Library for fast numerical vector and matrix calculations\n",
    "import numpy as np\n",
    "\n",
    "# Import matplotlib.pyplot for plotting graphs\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# This is a library extension to matplotlib to plot in 3D\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "\n",
    "# Import animation function for matplotlib and HTML for making HTML5 videos to display the animation in the browser\n",
    "from matplotlib.animation import FuncAnimation\n",
    "from IPython.display import HTML\n",
    "\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5f4433f",
   "metadata": {},
   "source": [
    "## Input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "3e092fbd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning! N is too small and has been set to N_min =  6000\n"
     ]
    }
   ],
   "source": [
    "#  Set final time T\n",
    "T = 7\n",
    "\n",
    "# Set the numer of time steps\n",
    "N = 1000\n",
    "\n",
    "# Determine the minimum number of time steps to have 60 fps\n",
    "# Since T is a float we need to make the final number an integer. \n",
    "# This is achieved by rounding up and then changing the datatype to int.\n",
    "N_min = int(np.ceil(T*60))\n",
    "\n",
    "# If N is too small, set it to N_min.\n",
    "# The number of time steps should not be lower than the number N_min of frames\n",
    "# in our animation for the desired animated time at 60 fps\n",
    "if N < N_min:\n",
    "    N = N_min\n",
    "    print(\"Warning! N is too small and has been set to N_min =\", N_min)\n",
    "\n",
    "# Set the time step (in s)\n",
    "dt = T/N\n",
    "\n",
    "# Define function for 2D trajectory\n",
    "# Input: - time t\n",
    "# output: - position vector at time t \n",
    "def trajectory(t):\n",
    "    # linear motion with velocity (1,1)\n",
    "    return np.array([t*np.cos(t),t*np.sin(t), np.cos(t)])\n",
    "\n",
    "# Ben's Spiral turned to Star: np.array([t*np.cos(t**2),t*np.sin(t**2)])\n",
    "\n",
    "# Aarav's Mystery: np.array([np.cos(t)**t-t,np.sin(t)])\n",
    "\n",
    "# Will's Mountain: np.array([t*np.cos(t)**3,t*np.sin(t)**2+7])\n",
    "\n",
    "# A simple spiral: np.array([t*np.cos(t)**2,t*np.sin(t)**2])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6274c61",
   "metadata": {},
   "source": [
    "##  Processing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "0ec1b38b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialise variables\n",
    "t = 0\n",
    "points = np.zeros((N+1,3))\n",
    "\n",
    "# Calculate the N points on the trajectory for times with a time step dt apart\n",
    "for i in range(N+1):\n",
    "  # call function trajectory with time t\n",
    "  points[i] = trajectory(t)\n",
    "  # save the new point in array points\n",
    "  # update the time by the time step\n",
    "  t += dt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e42cf419",
   "metadata": {},
   "source": [
    "## Output 2D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "828ba43a",
   "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": [
    "# print(points)\n",
    "\n",
    "# x axis values\n",
    "points_x = points[:,0]\n",
    "# corresponding y axis values\n",
    "points_y = points[:,1]\n",
    " \n",
    "# plotting the points\n",
    "plt.plot(points_x, points_y)\n",
    " \n",
    "# naming the x axis\n",
    "plt.xlabel('x - coordinate (m)')\n",
    "# naming the y axis\n",
    "plt.ylabel('y - coordinate (m)')\n",
    " \n",
    "# giving a title to my graph\n",
    "plt.title('Plot of a trajectory')\n",
    "\n",
    "# Hack to make x-scale and y-scale the same\n",
    "#plt.gca().set_aspect('equal', adjustable='box')\n",
    "\n",
    "# function to show the plot\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "df58e4b4",
   "metadata": {},
   "source": [
    "# Output 3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "0d5abb3b",
   "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": [
    "# We create a figure with 3D axes to plot the trajectory in 3D\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "# Like in 2D we have to save the x, y and z coordinates of the point particle in separate lists\n",
    "points_X = points[:,0]\n",
    "points_Y = points[:,1]\n",
    "points_Z = points[:,2]\n",
    "\n",
    "# Plot the 3D trajectory \n",
    "ax.plot(points_X, points_Y, points_Z)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10cd6e7d",
   "metadata": {},
   "source": [
    "## Output Animation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "77db4e1a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video width=\"432\" height=\"288\" controls autoplay loop>\n",
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      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create the figure object and axis object for this plot\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Create the line object that will be plotted in the animation\n",
    "ln, = plt.plot([], [])\n",
    "\n",
    "# Initialisation of the first frame for the animation\n",
    "\n",
    "# Work to do! Find a way how to determine the boundaries for the plot from the points numpy array holding \n",
    "# the data of the trajectory\n",
    "def init():\n",
    "    ax.set_xlim(-4, 7)\n",
    "    ax.set_ylim(-5, 5)\n",
    "    return ln,\n",
    "\n",
    "# Calculate the skipping rate for skipping frames\n",
    "skip_rate = N/N_min\n",
    "\n",
    "# Set the plotting data for the given frame skipping frames if necessary\n",
    "def animate(frame):\n",
    "    # We update the plot `ln` with the plotting data for the given frame and return it back to the caller\n",
    "    # The points of the particle have to be plotted until the time step that is calculated from the \n",
    "    # parameter `frame` as follows: The displayed time step = frame * skip_rate. We need to convert the \n",
    "    # resulting float into an integer. The data is obtained from the NumPy array points using slicing.\n",
    "    ln.set_data(points[:int(frame*skip_rate),0], points[:int(frame*skip_rate),1])\n",
    "    return ln,\n",
    "\n",
    "# This is the main function that creates an animation with the number of frames being \n",
    "# set to N_min (defined in the Input section) and a 16.7 ms delay between frames for a frame rate of 60 fps\n",
    "ani = FuncAnimation(fig, animate, frames=N_min,\n",
    "                    init_func=init,interval=16.7, blit=True)\n",
    "HTML(ani.to_html5_video())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73069ea4",
   "metadata": {},
   "source": [
    "## Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d26e04b9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 3 4 5]\n",
      "<class 'numpy.ndarray'>\n"
     ]
    }
   ],
   "source": [
    "arr = np.array([1, 2, 3, 4, 5])\n",
    "\n",
    "print(arr)\n",
    "\n",
    "print(type(arr))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0b9ad779",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TVE2nI/mN/nFRJG3N5o0fNxPftBZXdmjgdCTjZ2xEYBz3YXIGt7y1lIY1w5k3qqcVgbPw5LXt6RxVk4dmrWDrXmtOZ0rHCoFxjKry0tcbeWj2Cs5vXpvZI3sSVSvwGsf5QqUKoUwYFk9oqJA43ZrTmdKxQmAccfxkPg/OWsG4/21iUNco3r6tGzUrB27jOF+IqlWFlwfHsn73QZ74aLXTcYwfsUJgfC7nqKtx3NzlO3jw8tb8a1DnoGgc5wuXtqnHHy9tyezkDD5Yts3pOMZP2MFi41Pb9x/ltreXsn3/MV4ZHMv1cY2djhRw7r2sNcu3H+CJj9fQoVFNOja2Yy7m9OzPMOMzy7dl03/CAvYePsHUO7tZEfCS0BDhlcGx1KlakcTpyeQcteZ05vSsEBif+HL1boZMXkzliqHMSexpLRG8rE61Srx+Uzy7DuTy4OxUCgr8q4OA8S0rBMarVJX//LSZxOnJtGtYw904rprTsYJC16a1ePzqdnyzLpNJP/7idBxTjtkxAuM1+QXKM5+u4d1F6fTp0ICXB8da4zgfu61nDEnp2bz43w3ERkcEdQtvUzIbERivOHL8JCOmJvHuonTuvrAZE4bFWxFwgIjw/MDONKtblbEzl7PnYK7TkUw5ZIXAlLnMg7kMnryI7zZk8rd+HXj86vaEWOM4x1SrVMHdnC6fMTNSyLPmdKYIKwSmTG3YfYjrxy9gc9YRptySwM09YpyOZIDW9avz3MBOLNvquoaBMYXZMQJTZn7etJfEaclUruhqHGfnr5cv/WIbk5yezZSfttC1aS36dGzodCRTTtiIwJSJWcu2c9vbS2kUUZmPRveyIlBOPX51O7pER/Dw7JVsseZ0xs0KgTknqsqL/93AI3NW0qNFHWYn9qBRRGWnY5kSnGpOVyFUSJyWzLET1pzOWCEw5+D4yXzu+yCV179LY8h50bx123nUCLfGceVd44jKvDIkjg17DvGXj1bjb5erNWXPCoE5K9lHTnDzf5bycepOHr6yDc8O6ERYqG1O/uLi1pGM7d2KOSkZvL9su9NxjMPsYLEptfR9R7j97WVkZB/j1SGx9Iu1nkH+aOwfWpGyLZunPl5Dx0Y17YJAQcz+hDOlkpyeTf8JC9l/9ATT7jrfioAfCw0RXh0SR91qruZ0B46ecDqScYgVAuOxL1bt4qYpi6keXoG5iT3p1qy205HMOapdtSLjh8Wz52AuD8xaYc3pgpQVAnNGqsrkH39h1IwUOjSqwdzEnjSPtMZxgSKuSS3+cnV7vl2fycQfrDldMPJaIRCRcBFZKiIrRGSNiDxdzDIiIuNEJE1EVopIvLfymLNzMr+AJz5ezT/nr6dvx4bMuLs7dapVcjqWKWO39GjKtV0a8e+vNrAgba/TcYyPeXNEcBzorapdgFigj4h0L7LMVUAr920EMNGLeUwpHTl+krunJjFt8Tbuubg5rw2NIzzMGscFIhHhuQGdaB5ZjbEzl7M7x5rTBROvFQJ1Oex+GOa+Fd0B2Q+Y6l52MRAhIva793Jgd04uN0xaxI+b9vKP/h159Kp21jguwFWtVIFJw+M5lmfN6YKNV48RiEioiKQCmcDXqrqkyCKNgcInMWe4pxVdzwgRSRKRpKysLK/lNS7rdh2k/4QFpO87wn9uTWDY+U2djmR8pGW96jw/sDNJ6dk894U1pwsWXi0EqpqvqrFAFNBNRDoWWaS4PzF/d9qCqk5W1QRVTYiMjPRCUnPKDxuzuGHSIgpUmTWyB5e2qed0JONj13ZpxG09Y3jz5y3MX7XL6TjGB3xy1pCqHgC+B/oUmZUBRBd6HAXs9EUm83szl27jjneWEVXL1TiuQyP7gVGweqxvO+KaRPDIhyvZnHX4zE8wfs2bZw1FikiE+35l4DKg6FjzE+AW99lD3YEcVbU/QXysoEB54cv1PDp3Fb1a1mX2yB40rGmN44JZxQohjL8pnooVQkiclsLREyedjmS8yJsjgobAdyKyEliG6xjBZyIyUkRGupeZD2wG0oApwCgv5jHFyM3LZ+z7y5nw/S8M7daEN29NoLo1jjNAo4jKvDoklo2Zh3h8njWnC2Re6zWkqiuBuGKmTyp0X4HR3spgTm//kROMmJpEUno2f76qLfdc1BwROzPI/OrCVpHc94fWvPzNRro2rcXw7nbiQCCypnNBauveI9z+zjJ2HDjGa0PjuLZLI6cjmXLqj71bkrItm2c+XUvnqJp0jopwOpIpY9ZiIgglp++n/4QFHDh6ghl3nW9FwJxWSIjwyuBYIqtXInFaCtlHrDldoLFCEGQ+W7mToVOWULNyGPNG9SIhxhrHmTOr5W5Ol3kol/tnpVpzugBjhSBIqCoTv/+FMTOW07lxTeaO6kVM3apOxzJ+JDY6gievac/3G7IY/12a03FMGbJjBEHA1ThuDTOXbuPaLo3416DO1jPInJXh3ZuSlJ7NS99sJK5JLS5oVdfpSKYM2IggwB0+fpI7301i5tJtjLqkBa8OjrUiYM6aiPDsgE60qleNse8vZ1fOMacjmTJghSCA7co5xg2TFvFz2l6eHdCJR/q0tcZx5pxVqViBicO7cjwvn9HTUzhx0prT+TsrBAFqzc4crh+/gO37j/LWbecxtFsTpyOZANIishovDOpCyrYDPPvFOqfjmHNkhSAAfbchkxsnLSJEhNkje3Bxa2vUZ8re1Z0bcnuvGN5esJXPVlqLMH9mhSDATF+Szl3vJtG0TlXmjepFu4Y1nI5kAtijV7UjvkkEf/pwJWmZ1pzOX1khCBAFBcqzX6zj8XmruahVXWaN7EGDmuFOxzIBrmKFEMYPi6dSWCijpidbczo/dcZCICJVRSTEfb+1iFwnItaVrBzJzcvnjzOX88YPmxl2fhOm3JJAtUp2ZrDxjYY1KzNuSBybMg/z6NxV1pzOD3kyIvgRCBeRxsD/gNuBd7wZynhu3+Hj3DRlMZ+v2sVjfdvy9+s7UiHUBnrGty5oVZcHLmvNx6k7mbY43ek4ppQ8+cYQVT0KDABeU9X+QHvvxjKe2Jx1mAETF7Jm50EmDItnxEUtrHuocczoS1tyaZtInvlsLanbDzgdx5SCR4VARHoAw4DP3dNsv4PDlm7Zz4CJCzmUe5IZd3enb6eGTkcyQS4kRHh5cCz1qoczero1p/MnnhSC+4BHgXmqukZEmgPfeTWVOa2PU3cw/D9LqF2lIvNG9aRr01pORzIGgIgqFZk4PJ6sQ8e57wNrTucvzlgIVPUHVb1OVZ93P96sqmO9H80UpaqM/y6Ne99PJTY6grmjetK0jjWOM+VL56gInry2PT9szOK1b605nT8ocRePiLyiqveJyKfA78q6ql7n1WTmN/LyC/jLvNV8kLSdfrGNeGFQZypVsJ5Bpnwadn4TUtKzeeV/G4lrEsFF9qPGcu10+/rfc//3RV8EMSU7mJvH6Okp/LRpL3/s3ZIHLm9tB4VNuSYi/KN/J9bsPMi97y/n87EX0iiistOxTAlK3DWkqsnuu+vcu4f+/wbs9k08s/PAMW6ctIhFv+zjhYGdefCKNlYEjF+oXDGUicPjyctXRllzunLNk4PFP4nIjaceiMiDwDzvRTKnrN7hahy3I/sY79zejRvPi3Y6kjGl0jyyGi8M6kzq9gP8c741pyuvPCkElwA3i8hsEfkRaA1082oqw7fr93DjG4uoECJ8mNjTLgBi/FbfTg2584JmvLNwK5+ssOZ05ZEnZw3tAr4EegAxwFRVte5SXvTeoq3c9W4SzSOrMm90L9o0qO50JGPOyZ+vaktC01r8ec5K0jIPOR3HFOFJr6GvgfOBjkBf4GURsQPIXlBQoPzj87U88fEaLm1Tjw9G9KB+DWscZ/xfWGgIr98UT5WKoYyclsKR49acrjzxZNfQeFW9RVUPqOpqoCeQc6YniUi0iHwnIutEZI2I3FvMMpeISI6IpLpvT57FewgIuXn5jJ6RwpSftnBLj6ZMviWBqtY4zgSQBjXDGTckjs1Zh/mzNacrV874TaOqHxV5fBL4mwfrPgk8qKopIlIdSBaRr1V1bZHlflLVazwNHIj2Hj7O3VOTSN1+gL9c3Y47L2hmZwaZgNSzZV0evKIN//rvBhKa1uLWnjFORzJ4tmuou4gsE5HDInJCRPJF5IwjAlXdpaop7vuHgHVA43OPHFjSMg/Tf8IC1u06yMRhXbnrwuZWBExAS7y4BX9oW4+/f76WlG3ZTscxeLZr6HVgKLAJqAzcBYwvzYuISAwQBywpZnYPEVkhIl+ISIcSnj9CRJJEJCkrK6s0L12uLdm8j4ETF3L0eD4z7+5On44NnI5kjNeFhAgv3RhL/RrhjJmewn5rTuc4jxrXq2oaEKqq+ar6Nq5TSj0iItWAOcB9qnqwyOwUoKmqdgFeAz4q4fUnq2qCqiZERgbGT9U/Wr6Dm99cSt1qFZk3qhdxTaxxnAkeNauEMXFYV/YePsG97y8n35rTOcqTQnBURCoCqSLygojcD3jU6cx9JbM5wHRVnVt0vqoePHUqqqrOB8JEJKBPmFdVXvvfJu77IJX4phHMTexFkzpVnI5ljM91iqrJ0/068NOmvYz73yan4wQ1TwrBze7lxgBHgGhg4JmeJK4d3W/ialHxUgnLNHAvh4h0c7/OPs+i+5+8/AIe+XAl//56I/3jGvPuHd2oWcWu+mmC15DzohkYH8W4bzfx/YZMp+MELU/OGjp13blc4OlSrLsXriKySkRS3dMeA5q41zsJGAQkishJ4BgwRAP0nLKcY3mMmp7MgrR9jP1DK+6/rJUdFDZBT0T4+/UdWbMzh/s+SOXzsRfS2JrT+Zz42/duQkKCJiUlOR2jVDKyj3LHO8vYnHWE5wZ2ZlDXKKcjGVOubNl7hOte+5nm9aox657u1mLdC0QkWVUTiptnVzn3spUZB+g/YSG7cnJ5945uVgSMKUazulX51w2dWbH9AP/43JrT+VqpCoGI2PmNpfDN2j0MfmMxFUNDmJvYk14tA/o4uDHnpE/Hhtx9YTOmLkrn49QdTscJKqUdEcz3SooA9O7CrYx4L4lW9asxb3RPWtW3xnHGnMkjfdpyXkwt/jxnFRv3WHM6XyltIbCjm2eQX6A88+lanvpkDb3b1uf9Ed2pV90axxnjiVPN6apWqsDIackctuZ0PlHaQjDFKykCxLET+SROS+atBVu4vVcMb9zclSoVrXGcMaVRv0Y4rw2NY+veI/xpzkprTucDpSoEqjrBW0H8Xdah4wyZvIiv1+3hyWva89S1HQgNsQGUMWejR4s6PHRlGz5fuYt3Fm51Ok7Asz9Xy0Ba5iFue3sZew8f543hXbmigx1TN+ZcjbyoBSnp2fzj83V0joqga1Nrw+ItdvroOVr4y14GTFhIbl4BH4zoYUXAmDISEiL8+4ZYGkaEM2ZGCvsOH3c6UsDypA31GBGxUlyMOckZ3PrWUurVCGfeqJ50iY5wOpIxAeVUc7p9R05w7/up1pzOSzwZETQAlonILBHpI9YXAVXllW828uDsFZwXU5s5iT2Jrm2N44zxho6Na/K3fh34OW0vr36z0ek4AcmTi9f/BWiFq4HcbcAmEfmniLTwcrZy6cTJAh6cvYJXvtnEwPgo3rm9GzUrW+M4Y7xp8HlNuKFrFOO+TeM7a05X5jy9HoECu923k0At4EMRecGL2cqdnGN53PrWUuam7OD+y1rz4g2dqVjBDrMY4wt/u74j7RrW4P4PUsnIPup0nIDiyTGCsSKSDLwALAA6qWoi0BUP2lEHiu37jzJw4kKS0vfz0o1duNe6hxrjU+FhoUwcFk9+vjJqegrHT+Y7HSlgePLnbF1ggKpeqaqzVTUPQFULgKC46PyK7QfoP2EBmQdzmXrH+QyIt8Zxxjghpm5VXryxCyszcvjbZ2udjhMwPDlG8GShaxIUnRfwbQK/WrObwZMXER4WytxRPenRoo7TkYwJald2aMA9FzVn2uJtfLTcmtOVBdvBfRpv/byFe6Yl06ZBDeaN6kXLetY4zpjy4OEr29CtWW0enbuKDbutOd25skJQjPwC5a+frOGZz9ZyRfv6vH93dyKrV3I6ljHGrUJoCK8PjaNqpQokTkvmUG6e05H8mhWCIo6eOMk97yXzzsKt3HlBMyYM60rlina1JGPKm3o1wnn9pjjS9x+15nTnyApBIZmHchn8xmK+Xb+HZ/p14Ilr2lvjOGPKse7N6/DwlW2Yv2o3by3Y6nQcv2VN59w27jnE7W8vY/+RE0y5JYE/tKvvdCRjjAfuuag5yenZPDt/HV2iapIQU9vpSH7HRgTAgrS9DJy4kBP5Bcy6p4cVAWP8iIjw4g1daFyrMqNnpLDXmtOVWtAXgtlJ27n1raU0rBnOR6N70SmqptORjDGlVLOyqzndgaN53Pv+cmtOV0pBWwhUlZe+2sDDH66ke/M6fJjYk8YRlZ2OZYw5S+0b1eBv13dkQdo+Xv7amtOVRlAeIzh+Mp8/z1nFvOU7uDEhin/070RYaNDWRGMCxo0J0SRvzeb179KIbxpB77a2m9cTXvv2E5FoEflORNaJyBoRubeYZURExolImoisFJF4b+U5JedoHre8uZR5y3fw0BWteX5gZysCxgSQp/t1oH3DGtz/wQq277fmdJ7w5jfgSeBBVW0HdAdGi0j7IstchavFdStgBDDRi3nYtu8o/ScuYPm2A7w6JJYxva1xnDGBJjwslEnDu1KgruZ0uXnWnO5MvFYIVHWXqqa47x8C1gGNiyzWD5iqLouBCBFp6I08qe7GcfsOn+C9O7vRL7ZoFGNMoGhSpwov3RjLqh05PGPN6c7IJ/tERCQGiAOWFJnVGNhe6HEGvy8WiMgIEUkSkaSsrKyzywDUrVaJuaN6cn5zaxxnTKC7vH19Rl7cghlLtjEnOcPpOOWa1wuBiFQD5gD3qerBorOLecrvzvtS1cmqmqCqCZGRkWeVo0t0BF/ceyEtIqud1fONMf7noSta0715bR7/aBXrdxf9+jGneLUQiEgYriIwXVXnFrNIBhBd6HEUsNNbeUKsXYQxQaVCaAjjhsZRIzyMxGkpHLTmdMXy5llDgus6x+tU9aUSFvsEuMV99lB3IEdVd3krkzEm+NSrHs7rN8Wzbf9RHpltzemK480RQS/gZqC3iKS6b31FZKSIjHQvMx/YDKQBU4BRXsxjjAlS3ZrV5k992vDlmt28+fMWp+OUO177QZmq/kzxxwAKL6PAaG9lMMaYU+6+sDkp6Qd49ov1dImO4DxrTvf/7JdUxpigICK8cENnomtVZvT0FLIOWXO6U6wQGGOCRo3wMCYO78rB3DzGzlzOyfwCpyOVC1YIjDFBpV3DGvz9+k4s2ryPl6w5HWCFwBgThAZ1jWJot2gmfP8L36zd43Qcx1khMMYEpaeu7UDHxjV4YFYq2/YFd3M6KwTGmKAUHhbKxGFdARg1Izmom9NZITDGBK3o2lV4eXAsq3cc5OlP1zgdxzFWCIwxQe0P7eoz6pIWzFy6ndlJ28/8hABkhcAYE/QeuLw1PZrX4S8frWbtzuBrTmeFwBgT9E41p6tZOYxR05ODrjmdFQJjjAEiq1di/LB4tmcf46FZK4KqOZ0VAmOMcTsvpjaPXtWWr9buYcpPm52O4zNWCIwxppA7L2hG304NeP7LDSzZvM/pOD5hhcAYYwoREZ4f2JmmtaswZuZyMg/lOh3J66wQGGNMEdXDw5gwPJ5DuXn8cUbgN6ezQmCMMcVo26AG/+zfiSVb9vPiV4HdnM4KgTHGlGBAfBQ3nd+EST/8wtcB3JzOCoExxpzGk9e0p1PjmjwwK5X0fUecjuMVVgiMMeY0wsNCmTAsnhAREqelBGRzOisExhhzBq7mdF1Yu+sgT30ceM3prBAYY4wHeretz5hLW/JB0nZmLQus5nRWCIwxxkP3X96aXi3r8MTHq1mzM8fpOGXGCoExxngoNER4dUgctapUJHFaCjnHAqM5nRUCY4wphbrVKjF+WBw7DxzjodmB0ZzOa4VARN4SkUwRWV3C/EtEJEdEUt23J72VxRhjylLXprV5rG87vl67hzd+9P/mdN4cEbwD9DnDMj+paqz79owXsxhjTJm6vVcMV3duyAtfrmexnzen81ohUNUfgf3eWr8xxjjpVHO6mLpVGTNjOZkH/bc5ndPHCHqIyAoR+UJEOpS0kIiMEJEkEUnKysryZT5jjClRtUoVmDS8K0eOn2TMTP9tTudkIUgBmqpqF+A14KOSFlTVyaqaoKoJkZGRvspnjDFn1Lp+dZ4d0ImlW/bzr/9ucDrOWXGsEKjqQVU97L4/HwgTkbpO5THGmLN1fVxjhndvwhs/bua/a3Y7HafUHCsEItJARMR9v5s7i38fcTHGBK0nrmlPl6iaPDRrBVv3+ldzOm+ePjoTWAS0EZEMEblTREaKyEj3IoOA1SKyAhgHDNFAOCHXGBOUKlUIZfyweEJDhcTp/tWcTvztuzchIUGTkpKcjmGMMcX6bkMmd7yzjIHxUfxrUGfcOz4cJyLJqppQ3DynzxoyxpiAcmmbevzx0pZ8mJzBB37SnM4KgTHGlLF7L2vNha3q8uQna1i9o/w3p7NCYIwxZSw0RHhlcCx1qlYkcXoyOUfLd3M6KwTGGOMFdapVYvyweHbn5PLg7FQKCsrv8VgrBMYY4yXxTWrxeN92fLMuk0k//uJ0nBJZITDGGC+6tWcM13ZpxIv/3cDCX/Y6HadYVgiMMcaLRITnBnSiWd2qjJ25nD3lsDmdFQJjjPGyqu7mdEdP5DNmRgp55aw5nRUCY4zxgVbu5nTLtmbzwpfrnY7zG1YIjDHGR/rFNuaWHk2Z8tMWvly9y+k4/88KgTHG+NDjV7ejS3QED89eyZZy0pzOCoExxvhQpQqhTBgWT4VQIXFaMsdOON+czgqBMcb4WOOIyrwyJI4New7x+EercLr5pxUCY4xxwMWtIxnbuxVzU3Ywc6mzzemsEBhjjEPG/qEVF7WO5K+frGFVhnPN6awQGGOMQ041p6tbzdWc7sDRE47ksEJgjDEOql21IhOGd2XPwVwemLXCkeZ0VgiMMcZhsdERPHFNe75dn8nEH3zfnM4KgTHGlAM3d2/KdV0a8e+vNrAgzbfN6awQGGNMOSAiPDugE80jqzF25nJ25/iuOZ0VAmOMKSdczeniOZbn2+Z0VgiMMaYcaVmvOs8P7ExSejbPfeGb5nRWCIwxppy5tksjbusZw5s/b2H+Ku83p7NCYIwx5dBjfdsR1ySCRz5cyeasw159La8VAhF5S0QyRWR1CfNFRMaJSJqIrBSReG9lMcYYf1OxQgjjb4qnYoUQEqelcPTESa+9ljdHBO8AfU4z/yqglfs2ApjoxSzGGON3GkVU5tUhsWzMPMTj81Z7rTmd1wqBqv4I7D/NIv2AqeqyGIgQkYbeymOMMf7owlaR3H9Za+Yt38H0Jdu88hoVvLJWzzQGCrfcy3BP+92REREZgWvUQJMmTXwSzhhjyosxl7ZkU+ZhIqtX8sr6nSwEUsy0Ysc9qjoZmAyQkJDgbONuY4zxsZAQ4bWhcd5bv9fWfGYZQHShx1HAToeyGGNM0HKyEHwC3OI+e6g7kKOq5edqzsYYEyS8tmtIRGYClwB1RSQDeAoIA1DVScB8oC+QBhwFbvdWFmOMMSXzWiFQ1aFnmK/AaG+9vjHGGM/YL4uNMSbIWSEwxpggZ4XAGGOCnBUCY4wJcuKt3hXeIiJZQPpZPr0u4NtrwHmmvOaC8pvNcpWO5SqdQMzVVFUji5vhd4XgXIhIkqomOJ2jqPKaC8pvNstVOpardIItl+0aMsaYIGeFwBhjglywFYLJTgcoQXnNBeU3m+UqHctVOkGVK6iOERhjjPm9YBsRGGOMKcIKgTHGBLmAKAQi8paIZIrI6hLmi4iME5E0EVkpIvGF5vURkQ3ueX/2ca5h7jwrRWShiHQpNG+riKwSkVQRSfJxrktEJMf92qki8mSheU5+Xg8XyrRaRPJFpLZ7njc/r2gR+U5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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# importing the required module\n",
    "import matplotlib.pyplot as plt\n",
    " \n",
    "# x axis values\n",
    "x = [1,2,3]\n",
    "# corresponding y axis values\n",
    "y = [2,4,1]\n",
    " \n",
    "# plotting the points\n",
    "plt.plot(x, y)\n",
    " \n",
    "# naming the x axis\n",
    "plt.xlabel('x - axis')\n",
    "# naming the y axis\n",
    "plt.ylabel('y - axis')\n",
    " \n",
    "# giving a title to my graph\n",
    "plt.title('My first graph!')\n",
    " \n",
    "# function to show the plot\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "b089edc0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 1.]\n"
     ]
    }
   ],
   "source": [
    "# x axis values\n",
    "points_x = points[0]\n",
    "# corresponding y axis values\n",
    "points_y = [2,4,1]\n",
    "\n",
    "print(points_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "76b0edff",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.animation import FuncAnimation\n",
    "from IPython.display import HTML\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "xdata, ydata = [], []\n",
    "ln, = plt.plot([], [])\n",
    "\n",
    "def init():\n",
    "    ax.set_xlim(0, 2*np.pi)\n",
    "    ax.set_ylim(-1, 1)\n",
    "    return ln,\n",
    "\n",
    "def update(frame):\n",
    "    xdata.append(frame)\n",
    "    ydata.append(np.sin(frame))\n",
    "    ln.set_data(xdata, ydata)\n",
    "    return ln,\n",
    "\n",
    "ani = FuncAnimation(fig, update, frames=np.linspace(0, 2*np.pi, 128),\n",
    "                    init_func=init, blit=True)\n",
    "HTML(ani.to_html5_video())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "53eefdda",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <source type=\"video/mp4\" src=\"data:video/mp4;base64,AAAAHGZ0eXBNNFYgAAACAGlzb21pc28yYXZjMQAAAAhmcmVlAABiB21kYXQAAAKuBgX//6rcRem9\n",
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       "  Your browser does not support the video tag.\n",
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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from matplotlib import animation\n",
    "from IPython.display import HTML\n",
    "\n",
    "# First set up the figure, the axis, and the plot element we want to animate\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.set_xlim(( 0, 2))\n",
    "ax.set_ylim((-2, 2))\n",
    "\n",
    "line, = ax.plot([], [], lw=5)\n",
    "\n",
    "# initialization function: plot the background of each frame\n",
    "def init():\n",
    "    # line.set_data([], [])\n",
    "    return (line,)\n",
    "\n",
    "# animation function. This is called sequentially\n",
    "def animate(i):\n",
    "    x = np.linspace(0, 2, 1000)\n",
    "    y = np.sin(2 * np.pi * (x - 0.01 * i))\n",
    "    line.set_data(x, y)\n",
    "    return (line,)\n",
    "# call the animator. blit=True means only re-draw the parts that have changed.\n",
    "anim = animation.FuncAnimation(fig, animate, init_func=init,\n",
    "                               frames=100, interval=20, blit=True)\n",
    "HTML(anim.to_html5_video())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a9de3452",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[1;31mType:\u001b[0m           Line2D\n",
       "\u001b[1;31mString form:\u001b[0m    Line2D(_line0)\n",
       "\u001b[1;31mFile:\u001b[0m           c:\\programdata\\anaconda3\\lib\\site-packages\\matplotlib\\lines.py\n",
       "\u001b[1;31mDocstring:\u001b[0m     \n",
       "A line - the line can have both a solid linestyle connecting all\n",
       "the vertices, and a marker at each vertex.  Additionally, the\n",
       "drawing of the solid line is influenced by the drawstyle, e.g., one\n",
       "can create \"stepped\" lines in various styles.\n",
       "\u001b[1;31mInit docstring:\u001b[0m\n",
       "Create a `.Line2D` instance with *x* and *y* data in sequences of\n",
       "*xdata*, *ydata*.\n",
       "\n",
       "Additional keyword arguments are `.Line2D` properties:\n",
       "\n",
       "Properties:\n",
       "    agg_filter: a filter function, which takes a (m, n, 3) float array and a dpi value, and returns a (m, n, 3) array\n",
       "    alpha: float or None\n",
       "    animated: bool\n",
       "    antialiased or aa: bool\n",
       "    clip_box: `.Bbox`\n",
       "    clip_on: bool\n",
       "    clip_path: Patch or (Path, Transform) or None\n",
       "    color or c: color\n",
       "    contains: unknown\n",
       "    dash_capstyle: {'butt', 'round', 'projecting'}\n",
       "    dash_joinstyle: {'miter', 'round', 'bevel'}\n",
       "    dashes: sequence of floats (on/off ink in points) or (None, None)\n",
       "    data: (2, N) array or two 1D arrays\n",
       "    drawstyle or ds: {'default', 'steps', 'steps-pre', 'steps-mid', 'steps-post'}, default: 'default'\n",
       "    figure: `.Figure`\n",
       "    fillstyle: {'full', 'left', 'right', 'bottom', 'top', 'none'}\n",
       "    gid: str\n",
       "    in_layout: bool\n",
       "    label: object\n",
       "    linestyle or ls: {'-', '--', '-.', ':', '', (offset, on-off-seq), ...}\n",
       "    linewidth or lw: float\n",
       "    marker: marker style string, `~.path.Path` or `~.markers.MarkerStyle`\n",
       "    markeredgecolor or mec: color\n",
       "    markeredgewidth or mew: float\n",
       "    markerfacecolor or mfc: color\n",
       "    markerfacecoloralt or mfcalt: color\n",
       "    markersize or ms: float\n",
       "    markevery: None or int or (int, int) or slice or List[int] or float or (float, float) or List[bool]\n",
       "    path_effects: `.AbstractPathEffect`\n",
       "    picker: unknown\n",
       "    pickradius: float\n",
       "    rasterized: bool or None\n",
       "    sketch_params: (scale: float, length: float, randomness: float)\n",
       "    snap: bool or None\n",
       "    solid_capstyle: {'butt', 'round', 'projecting'}\n",
       "    solid_joinstyle: {'miter', 'round', 'bevel'}\n",
       "    transform: `matplotlib.transforms.Transform`\n",
       "    url: str\n",
       "    visible: bool\n",
       "    xdata: 1D array\n",
       "    ydata: 1D array\n",
       "    zorder: float\n",
       "\n",
       "See :meth:`set_linestyle` for a description of the line styles,\n",
       ":meth:`set_marker` for a description of the markers, and\n",
       ":meth:`set_drawstyle` for a description of the draw styles.\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "line?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "19f4d487",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[1;31mType:\u001b[0m            ndarray\n",
       "\u001b[1;31mString form:\u001b[0m    \n",
       "[[ 0.00000000e+00  0.00000000e+00  1.00000000e+00]\n",
       "           [ 1.00000000e-03  1.00000000e-09  1.00000000e <...> 51935098e+00 -5.23456396e+00  8.52020300e-01]\n",
       "           [ 8.62318872e+00 -5.06365641e+00  8.62318872e-01]]\n",
       "\u001b[1;31mLength:\u001b[0m          10001\n",
       "\u001b[1;31mFile:\u001b[0m            c:\\programdata\\anaconda3\\lib\\site-packages\\numpy\\__init__.py\n",
       "\u001b[1;31mDocstring:\u001b[0m       <no docstring>\n",
       "\u001b[1;31mClass docstring:\u001b[0m\n",
       "ndarray(shape, dtype=float, buffer=None, offset=0,\n",
       "        strides=None, order=None)\n",
       "\n",
       "An array object represents a multidimensional, homogeneous array\n",
       "of fixed-size items.  An associated data-type object describes the\n",
       "format of each element in the array (its byte-order, how many bytes it\n",
       "occupies in memory, whether it is an integer, a floating point number,\n",
       "or something else, etc.)\n",
       "\n",
       "Arrays should be constructed using `array`, `zeros` or `empty` (refer\n",
       "to the See Also section below).  The parameters given here refer to\n",
       "a low-level method (`ndarray(...)`) for instantiating an array.\n",
       "\n",
       "For more information, refer to the `numpy` module and examine the\n",
       "methods and attributes of an array.\n",
       "\n",
       "Parameters\n",
       "----------\n",
       "(for the __new__ method; see Notes below)\n",
       "\n",
       "shape : tuple of ints\n",
       "    Shape of created array.\n",
       "dtype : data-type, optional\n",
       "    Any object that can be interpreted as a numpy data type.\n",
       "buffer : object exposing buffer interface, optional\n",
       "    Used to fill the array with data.\n",
       "offset : int, optional\n",
       "    Offset of array data in buffer.\n",
       "strides : tuple of ints, optional\n",
       "    Strides of data in memory.\n",
       "order : {'C', 'F'}, optional\n",
       "    Row-major (C-style) or column-major (Fortran-style) order.\n",
       "\n",
       "Attributes\n",
       "----------\n",
       "T : ndarray\n",
       "    Transpose of the array.\n",
       "data : buffer\n",
       "    The array's elements, in memory.\n",
       "dtype : dtype object\n",
       "    Describes the format of the elements in the array.\n",
       "flags : dict\n",
       "    Dictionary containing information related to memory use, e.g.,\n",
       "    'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.\n",
       "flat : numpy.flatiter object\n",
       "    Flattened version of the array as an iterator.  The iterator\n",
       "    allows assignments, e.g., ``x.flat = 3`` (See `ndarray.flat` for\n",
       "    assignment examples; TODO).\n",
       "imag : ndarray\n",
       "    Imaginary part of the array.\n",
       "real : ndarray\n",
       "    Real part of the array.\n",
       "size : int\n",
       "    Number of elements in the array.\n",
       "itemsize : int\n",
       "    The memory use of each array element in bytes.\n",
       "nbytes : int\n",
       "    The total number of bytes required to store the array data,\n",
       "    i.e., ``itemsize * size``.\n",
       "ndim : int\n",
       "    The array's number of dimensions.\n",
       "shape : tuple of ints\n",
       "    Shape of the array.\n",
       "strides : tuple of ints\n",
       "    The step-size required to move from one element to the next in\n",
       "    memory. For example, a contiguous ``(3, 4)`` array of type\n",
       "    ``int16`` in C-order has strides ``(8, 2)``.  This implies that\n",
       "    to move from element to element in memory requires jumps of 2 bytes.\n",
       "    To move from row-to-row, one needs to jump 8 bytes at a time\n",
       "    (``2 * 4``).\n",
       "ctypes : ctypes object\n",
       "    Class containing properties of the array needed for interaction\n",
       "    with ctypes.\n",
       "base : ndarray\n",
       "    If the array is a view into another array, that array is its `base`\n",
       "    (unless that array is also a view).  The `base` array is where the\n",
       "    array data is actually stored.\n",
       "\n",
       "See Also\n",
       "--------\n",
       "array : Construct an array.\n",
       "zeros : Create an array, each element of which is zero.\n",
       "empty : Create an array, but leave its allocated memory unchanged (i.e.,\n",
       "        it contains \"garbage\").\n",
       "dtype : Create a data-type.\n",
       "\n",
       "Notes\n",
       "-----\n",
       "There are two modes of creating an array using ``__new__``:\n",
       "\n",
       "1. If `buffer` is None, then only `shape`, `dtype`, and `order`\n",
       "   are used.\n",
       "2. If `buffer` is an object exposing the buffer interface, then\n",
       "   all keywords are interpreted.\n",
       "\n",
       "No ``__init__`` method is needed because the array is fully initialized\n",
       "after the ``__new__`` method.\n",
       "\n",
       "Examples\n",
       "--------\n",
       "These examples illustrate the low-level `ndarray` constructor.  Refer\n",
       "to the `See Also` section above for easier ways of constructing an\n",
       "ndarray.\n",
       "\n",
       "First mode, `buffer` is None:\n",
       "\n",
       ">>> np.ndarray(shape=(2,2), dtype=float, order='F')\n",
       "array([[0.0e+000, 0.0e+000], # random\n",
       "       [     nan, 2.5e-323]])\n",
       "\n",
       "Second mode:\n",
       "\n",
       ">>> np.ndarray((2,), buffer=np.array([1,2,3]),\n",
       "...            offset=np.int_().itemsize,\n",
       "...            dtype=int) # offset = 1*itemsize, i.e. skip first element\n",
       "array([2, 3])\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "points?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "52e5817f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 1., ..., 1., 1., 0.])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.append(points,[1,1,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "5990fc08",
   "metadata": {},
   "outputs": [],
   "source": [
    "T =1.00011\n",
    "N_min = int(np.ceil(T*60))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "42c3de78",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "61"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N_min"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "7c45db74",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "60.006600000000006"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T*60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "437c31b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int(0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "0acfa35e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int(0.7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "bf4aa3e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int(1.56)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "a2582e23",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "e5c1f0a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.380952380952381"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N/N_min"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "550e049d",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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