{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "f4419154",
   "metadata": {},
   "source": [
    "# Rotational motion\n",
    "- Börge Göbel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ce2064a4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ef2d44f8",
   "metadata": {},
   "source": [
    "## Rotation of a point mass around a point in space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e223f4db",
   "metadata": {},
   "outputs": [],
   "source": [
    " m = 1 ### Mass - SI unit: [m] = kg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "08e44d61",
   "metadata": {},
   "outputs": [],
   "source": [
    " r = 1 ### Radius - [r] = m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c6951e3b",
   "metadata": {},
   "outputs": [],
   "source": [
    " omega = 1 ### Angular velocity - [omega] = 1/s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c2ca2d1c",
   "metadata": {},
   "outputs": [],
   "source": [
    "t_array = np.linspace(0, 2*np.pi, 100)\n",
    "x_array = r*np.cos(omega*t_array)\n",
    "y_array = r*np.sin(omega*t_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "71d9de88",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1fba65cd820>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "ax.set_aspect(1)\n",
    "\n",
    "plt.xlabel('x coordinate')\n",
    "plt.ylabel('y coordinate')\n",
    "plt.plot(x_array,y_array)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f0c6b4be",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x1fba66f92b0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt3D = plt.axes(projection='3d')\n",
    "\n",
    "plt3D.set_xlabel('x coordinate [m]')\n",
    "plt3D.set_ylabel('y coordinate [m]')\n",
    "plt3D.set_zlabel('time [s]')\n",
    "plt3D.scatter3D(x_array, y_array, t_array)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b33634f",
   "metadata": {},
   "source": [
    "### Calculate energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ac7e0338",
   "metadata": {},
   "outputs": [],
   "source": [
    "period = 2*np.pi / omega"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "3017941c",
   "metadata": {},
   "outputs": [],
   "source": [
    "path = 2*np.pi * r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "54a2c6aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "# velocity = path / period\n",
    "velocity = r*omega"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9a23427",
   "metadata": {},
   "source": [
    "Rotation energy = kinetic energy "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e9cc0ec7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# m/2 * velocity**2\n",
    "m/2 * omega**2 * r**2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "947ba853",
   "metadata": {},
   "source": [
    "## Rotation energy of multiple point masses"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c6da35a",
   "metadata": {},
   "source": [
    "If we assume that all point masses belong to the same object, they have the same angular velocity omega.\n",
    "Only the radius differs."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a25e849",
   "metadata": {},
   "source": [
    "\\\\( E_\\mathrm{rot} = \\frac{I}{2}\\omega^2 \\\\) with \\\\( I = m \\sum_i r_i^2\\\\): Moment of inertia"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04f32220",
   "metadata": {},
   "source": [
    "### Rotating a stick around one end ( \\\\( I = \\frac{1}{3}ms^2 \\\\) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "7de36a3e",
   "metadata": {},
   "outputs": [],
   "source": [
    "s = 1### Length - Unit [s] = m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "5d0aae11",
   "metadata": {},
   "outputs": [],
   "source": [
    "num_points = 1000\n",
    "r_list = np.linspace(0,s,num_points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "0a80f64a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1fba67aa6d0>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "ax.set_aspect(1)\n",
    "\n",
    "plt.xlabel('x coordinate')\n",
    "plt.ylabel('y coordinate')\n",
    "plt.xlim([-1.2*s,1.2*s])\n",
    "plt.ylim([-1.2*s,1.2*s])\n",
    "plt.plot(r_list, np.zeros(num_points))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "975e8642",
   "metadata": {},
   "source": [
    "- analytical result:\n",
    "\n",
    " \\\\( E_\\mathrm{rot} = \\frac{I}{2}\\omega^2 = \\frac{1}{2}\\omega^2\\int\\mathrm{d}m\\, r^2\\\\)\n",
    "\n",
    " \\\\( I = \\int\\mathrm{d}m\\, r^2 \\quad\\quad\\quad \\text{with}\\quad \\mathrm{d}m = \\sigma\\,\\mathrm{d}r \\quad\\quad\\quad \\text{and}\\quad \\sigma = \\frac{m}{s}\\quad\\text{length density}\\\\)\n",
    " \n",
    " \\\\( I = \\frac{m}{s}\\int_0^s\\mathrm{d}r\\, r^2 \\\\)\n",
    " \n",
    " \\\\( I = \\frac{m}{s} \\frac{1}{3}[r^3]_{r=0}^{r=s}\\\\)\n",
    " \n",
    " \\\\( I = \\frac{1}{3}ms^2\\\\)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "eaf6ef7e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.16666666666666666"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1/3*m*s**2 / 2 * omega**2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c8c02bb",
   "metadata": {},
   "source": [
    "- numerical result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "3ca47f91",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.16675008341675007"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(m/num_points)/2 * omega**2 * np.sum(r_list**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "feb7d062",
   "metadata": {},
   "source": [
    "### Rotating a stick around the middle ( \\\\( I = \\frac{1}{12}ms^2 \\\\) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "12a0375b",
   "metadata": {},
   "outputs": [],
   "source": [
    "num_points = 1000\n",
    "r_list = np.linspace(-s/2,s/2,num_points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "ec621fee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1fba680e7f0>]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "ax.set_aspect(1)\n",
    "\n",
    "plt.xlabel('x coordinate')\n",
    "plt.ylabel('y coordinate')\n",
    "plt.xlim([-1.2*s,1.2*s])\n",
    "plt.ylim([-1.2*s,1.2*s])\n",
    "plt.plot(r_list, np.zeros(num_points))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3db03ed4",
   "metadata": {},
   "source": [
    "- analytical result:\n",
    "\n",
    " \\\\( E_\\mathrm{rot} = \\frac{I}{2}\\omega^2 = \\frac{1}{2}\\omega^2\\int\\mathrm{d}m\\, r^2\\\\)\n",
    "\n",
    " \\\\( I = \\int\\mathrm{d}m\\, r^2 \\quad\\quad\\quad \\text{with}\\quad \\mathrm{d}m = \\sigma\\,\\mathrm{d}r \\quad\\quad\\quad \\text{and}\\quad \\sigma = \\frac{m}{s}\\quad\\text{length density}\\\\)\n",
    " \n",
    " \\\\( I = \\frac{m}{s}\\int_{-s/2}^{s/2}\\mathrm{d}r\\, r^2 \\\\)\n",
    " \n",
    " \\\\( I = \\frac{m}{s} \\frac{1}{3}[r^3]_{r=-s/2}^{r=s/2}\\\\)\n",
    " \n",
    " \\\\( I = \\frac{m}{s} \\frac{1}{3}\\left[\\frac{s^3}{8}-\\left(-\\frac{s^3}{8}\\right)\\right]\\\\)\n",
    " \n",
    " \\\\( I = \\frac{1}{12}ms^2\\\\)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "0d4d7db5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.041666666666666664"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1/12*m*s**2 / 2 * omega**2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0069627f",
   "metadata": {},
   "source": [
    "- numerical result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "5de45c6d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.041750083416750086"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(m/num_points)/2 * omega**2 * np.sum(r_list**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4511634",
   "metadata": {},
   "source": [
    "### Rotating a sphere around the z axis ( \\\\( I = \\frac{2}{5}mR^2 \\\\) )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e39a9a8e",
   "metadata": {},
   "source": [
    "- analytical result\n",
    "\n",
    " \\\\( E_\\mathrm{rot} = \\frac{I}{2}\\omega^2 = \\frac{1}{2}\\omega^2\\int\\mathrm{d}m\\, r^2\\\\)\n",
    "\n",
    " \\\\( I = \\int\\mathrm{d}m\\, r^2 \\quad\\quad\\quad \\text{with}\\quad \\mathrm{d}m = \\rho\\,\\mathrm{d}V \\quad\\quad\\quad \\text{and}\\quad \\rho=\\frac{m}{V} \\quad\\text{(volume) density}\\\\)\n",
    " \n",
    " \\\\( I = \\frac{m}{V}\\int_V\\mathrm{d}V\\, r^2 \\\\)\n",
    " \n",
    " use cylindrical coordinates\n",
    " \n",
    " \\\\( I = \\frac{m}{V}\\int_{z=-R}^{R}\\int_{r=0}^{\\tilde{R}(z)}\\int_{\\varphi=0}^{2\\pi}\\,r\\,\\mathrm{d}r\\mathrm{d}z\\mathrm{d}\\varphi\\, r^2 \\\\)\n",
    " \n",
    " Calculate polar-angle integral and use \\\\( \\tilde{R}(z) = \\sqrt{R^2-z^2} \\\\)\n",
    " \n",
    "  \\\\( I = \\frac{m}{V} \\left(\\int_{\\varphi=0}^{2\\pi}\\,\\mathrm{d}\\varphi\\right)\\, \\int_{z=-R}^{R}\\int_{r=0}^{\\tilde{R}(z)} r^3 \\,\\mathrm{d}r\\mathrm{d}z\\\\)\n",
    "  \n",
    "  \\\\( I = \\frac{m}{V} 2\\pi\\,\\int_{z=-R}^{R} \\left[\\frac{1}{4}r^4\\right]_{r=0}^{\\sqrt{R^2-z^2}} \\,\\mathrm{d}z \\\\)\n",
    "  \n",
    "  \\\\( I = \\frac{m}{V} 2\\pi\\,\\int_{z=-R}^{R} \\frac{1}{4}\\left(R^2-z^2\\right)^2 \\,\\mathrm{d}z \\\\)\n",
    "  \n",
    "  \\\\( I = \\frac{m}{V} \\frac{\\pi}{2}\\,\\int_{z=-R}^{R} \\left(R^4-2R^2z^2+z^4\\right) \\,\\mathrm{d}z \\\\)\n",
    "  \n",
    "  \\\\( I = \\frac{m}{V} \\frac{\\pi}{2}\\,\\left[R^4z-\\frac{2}{3}R^2z^3+\\frac{1}{5}z^5\\right]_{z=-R}^{R} \\\\)\n",
    "  \n",
    "  \\\\( I = \\frac{m}{V} \\frac{\\pi}{2}\\,2\\left(R^5-\\frac{2}{3}R^5+\\frac{1}{5}R^5\\right) \\\\)\n",
    "  \n",
    "  \\\\( I = \\frac{m}{V} \\pi\\,\\frac{8}{15}R^5 \\\\)\n",
    "  \n",
    " use volume of the sphere \\\\( V = \\frac{4}{3}\\pi R^3 \\\\)\n",
    " \n",
    " \\\\( I = m \\frac{\\frac{8}{15}\\pi R^5}{\\frac{4}{3}\\pi R^3} \\\\)\n",
    " \n",
    " \\\\( I = \\frac{2}{5}mR^2\\\\)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "14abae1e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2/5*m*r**2 / 2 * omega**2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e966ed1b",
   "metadata": {},
   "source": [
    "- numerical result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "40905082",
   "metadata": {},
   "outputs": [],
   "source": [
    "num_points = 30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "522d1322",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "27000"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "30*30*30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "0b686d71",
   "metadata": {},
   "outputs": [],
   "source": [
    "coord_list = [] ### just for plotting\n",
    "counter = 0\n",
    "contribution = 0\n",
    "\n",
    "for x in np.linspace(-r,r,num_points):\n",
    "    for y in np.linspace(-r,r,num_points):\n",
    "        for z in np.linspace(-r,r,num_points):\n",
    "            if(np.linalg.norm([x,y,z]) <= r ):\n",
    "                coord_list.append([x,y,z]) ### just for plotting\n",
    "                counter = counter +1\n",
    "                contribution = contribution + np.linalg.norm([x,y,0])**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "23de2b4d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12712"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "a74ede99",
   "metadata": {},
   "outputs": [],
   "source": [
    "coord_list = np.transpose(coord_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "9fce7125",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x1fba68506a0>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt3D = plt.axes(projection='3d')\n",
    "\n",
    "plt3D.set_xlabel('x coordinate [m]')\n",
    "plt3D.set_ylabel('y coordinate [m]')\n",
    "plt3D.set_zlabel('z coordinate [m]')\n",
    "plt3D.scatter3D(coord_list[0],coord_list[1],coord_list[2],s=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "62662d8a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1993827959612327"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(m/counter) * contribution / 2 * omega**2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5213af6",
   "metadata": {},
   "source": [
    "### Rotating a spherical shell around the z axis ( \\\\( I = \\frac{2}{5}m\\frac{r_1^5-r_2^5}{r_1^3-r_2^3} \\\\) )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "484b9ed6",
   "metadata": {},
   "source": [
    "- analytical result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "036d127d",
   "metadata": {},
   "outputs": [],
   "source": [
    "r1 = 1\n",
    "r2 = 0.8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "948c181f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.27554098360655743"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1/2 * omega**2 * 2/5 * m * (r1**5 - r2**5)/(r1**3 - r2**3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a702874",
   "metadata": {},
   "source": [
    "- numerical result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "07e318f8",
   "metadata": {},
   "outputs": [],
   "source": [
    "num_points = 40"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "d1e9b106",
   "metadata": {},
   "outputs": [],
   "source": [
    "coord_list = [] ### just for plotting\n",
    "counter = 0\n",
    "contribution = 0\n",
    "\n",
    "for x in np.linspace(-r,r,num_points):\n",
    "    for y in np.linspace(-r,r,num_points):\n",
    "        for z in np.linspace(-r,r,num_points):\n",
    "            if(r2 <= np.linalg.norm([x,y,z]) <= r1 ):\n",
    "                coord_list.append([x,y,z]) ### just for plotting\n",
    "                counter = counter +1\n",
    "                contribution = contribution + np.linalg.norm([x,y,0])**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "7ff52b26",
   "metadata": {},
   "outputs": [],
   "source": [
    "coord_list = np.transpose(coord_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "d58e2b59",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x1fba42f7280>"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt3D = plt.axes(projection='3d')\n",
    "\n",
    "plt3D.set_xlabel('x coordinate [m]')\n",
    "plt3D.set_ylabel('y coordinate [m]')\n",
    "plt3D.set_zlabel('z coordinate [m]')\n",
    "plt3D.scatter3D(coord_list[0],coord_list[1],coord_list[2],s=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "187df6da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2755370034739556"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(m/counter) * contribution / 2 * omega**2"
   ]
  }
 ],
 "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
