Mechanics/Lab1 | Physical pendulum/Lab1 | Physical pendulum.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Вивчення фізичного маятника \n",
    "### Лабораторна робота №4\n",
    "\n",
    "Виконав студент групи ФІ-81 *Шкаліков Олег Володимирович*  \n",
    "Перевірив *Димитрієва Наталія Федорівна*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Мета**: Визначення прискорення вільного падіння за допомогою оборотного маятника  \n",
    "**Завдання**: \n",
    "- Виміряти період $T$, вимірявши час 5-10 коливань\n",
    "- Виміряти довжину нитки математичного маятника, період коливань якого співпадає з фізичним\n",
    "- Знайти прискорення вільного падіння $g$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Теоретична частина"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Фізичним маятником називають будь-яке тверде тіло, яке може вільно обертатись навколо горизонтальної осі під дією сили тяжіння. Рух будь-якого маятника описується рівнянням(1)\n",
    "$$M = J{\\partial^2\\phi \\over \\partial t^2}$$\n",
    ", де $J$ - момент інерції маятника, $\\phi$ - кут відхилення центра мас маятника від положення рівноваги, $M$ - момент сил, що діють на маятник, $t$ - час. \n",
    "![](PhysicsM.png)\n",
    "Наприклад, для однорідного стержня довжиною $l$ за теоремою Гюйгенса-Штейнера момент інерції дорівнює:\n",
    "$$J = ms^2 + {ml^2\\over12}$$\n",
    ", де $m$ - масса маятника, $s$ - відстань між центром мас та віссю обертання.  \n",
    "Момент сили тяжіння, що діє на маятник можна розрахувати за формулою\n",
    "$$M = -smg\\sin\\phi$$\n",
    "Якщо кут $\\phi$ - малий, тоді $\\sin \\phi \\approx \\phi$, отже \n",
    "$$M \\approx -smg \\phi$$\n",
    "Добре налагоджений маятник може зробити кілька сот коливань коливань без помітного згасання, тому моментом сили тертя в першому наближенні можна знехтувати. Підставляючи вираз для $M$ в (1), отримаємо рівняння для коливань(2):\n",
    "$$\\phi'' + \\omega^2\\phi = 0$$\n",
    "з частотою(3)\n",
    "$$\\omega = \\sqrt{mgs\\over J}$$\n",
    "Рівняння (2) описує гармонічні коливання, що відбуваєтся за законом $\\phi(t) = A \\sin(\\omega t + \\theta)$. Амплітуда коливань $A$ та їх фаза $\\theta$ залежать від способу збудження коливань, тобто від початкових умов. Власна частота коливань $\\omega$ згідно з (3), визначається тільки параметрами маятника $J$ та $s$.  \n",
    "Період коливань фізичного маятника $T = {2\\pi \\over \\omega}$, як і його частота, не залежить від фази та амплітуди коливань і дорівнює(4)\n",
    "$$T = 2\\pi \\sqrt{J\\over mgs}$$\n",
    "Рух маятника описуэться рівнянням гармонічних коливань(2) лише за умови малих коливань($\\sin \\phi \\approx \\phi$). Якщо ввсети позначення $L={J \\over ms}$, то формула буде мати такий вигляд, як і формула для математичного маятника(5)\n",
    "$$T = 2\\pi\\sqrt{L \\over g}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Практична частина"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для обрахунку, перетворення та візуалізації результатів експерименту будемо використовувати бібліотеки Pandas, Scipy, Numpy та Matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import scipy.linalg\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Вивантажимо дані експерименту, збережені у csv файлі, та представимо їх у вигляді таблиці"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>N</th>\n",
       "      <th>t(с)</th>\n",
       "      <th>s(см)</th>\n",
       "      <th>L(см)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>11</td>\n",
       "      <td>11.169</td>\n",
       "      <td>17.0</td>\n",
       "      <td>25.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>11</td>\n",
       "      <td>11.177</td>\n",
       "      <td>17.0</td>\n",
       "      <td>25.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>14</td>\n",
       "      <td>14.220</td>\n",
       "      <td>17.0</td>\n",
       "      <td>25.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>11</td>\n",
       "      <td>11.173</td>\n",
       "      <td>17.0</td>\n",
       "      <td>25.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>8</td>\n",
       "      <td>8.360</td>\n",
       "      <td>18.0</td>\n",
       "      <td>24.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>11</td>\n",
       "      <td>11.489</td>\n",
       "      <td>18.0</td>\n",
       "      <td>24.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>11</td>\n",
       "      <td>11.477</td>\n",
       "      <td>18.0</td>\n",
       "      <td>24.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>9.039</td>\n",
       "      <td>22.0</td>\n",
       "      <td>31.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>9.046</td>\n",
       "      <td>22.0</td>\n",
       "      <td>31.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>8</td>\n",
       "      <td>9.041</td>\n",
       "      <td>22.0</td>\n",
       "      <td>31.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>10</td>\n",
       "      <td>8</td>\n",
       "      <td>9.646</td>\n",
       "      <td>21.5</td>\n",
       "      <td>33.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>11</td>\n",
       "      <td>8</td>\n",
       "      <td>9.645</td>\n",
       "      <td>21.5</td>\n",
       "      <td>33.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>12</td>\n",
       "      <td>8</td>\n",
       "      <td>9.658</td>\n",
       "      <td>21.5</td>\n",
       "      <td>33.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     N    t(с)  s(см)  L(см)\n",
       "0   11  11.169   17.0   25.3\n",
       "1   11  11.177   17.0   25.3\n",
       "2   14  14.220   17.0   25.3\n",
       "3   11  11.173   17.0   25.3\n",
       "4    8   8.360   18.0   24.7\n",
       "5   11  11.489   18.0   24.7\n",
       "6   11  11.477   18.0   24.7\n",
       "7    8   9.039   22.0   31.0\n",
       "8    8   9.046   22.0   31.0\n",
       "9    8   9.041   22.0   31.0\n",
       "10   8   9.646   21.5   33.0\n",
       "11   8   9.645   21.5   33.0\n",
       "12   8   9.658   21.5   33.0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv(\"Lab1.csv\")\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ", де $N$ - кількість коливань, $t(c)$ - час, $s(cм)$ - довжина між центром мас та віссю коливань, $L(см)$ - довжина нитки математичного маятника, який коливається з періодом рівним періоду фізичного маятника.\n",
    "Обрахуємо середні значення колонок для рівних $L$ та приведемо дані у одиниці системи СІ та перейменуємо колонки для більш зручної роботи з ними"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>L</th>\n",
       "      <th>N</th>\n",
       "      <th>t</th>\n",
       "      <th>s</th>\n",
       "      <th>T</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.247</td>\n",
       "      <td>10.00</td>\n",
       "      <td>10.442000</td>\n",
       "      <td>0.180</td>\n",
       "      <td>1.044200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.253</td>\n",
       "      <td>11.75</td>\n",
       "      <td>11.934750</td>\n",
       "      <td>0.170</td>\n",
       "      <td>1.015723</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.310</td>\n",
       "      <td>8.00</td>\n",
       "      <td>9.042000</td>\n",
       "      <td>0.220</td>\n",
       "      <td>1.130250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.330</td>\n",
       "      <td>8.00</td>\n",
       "      <td>9.649667</td>\n",
       "      <td>0.215</td>\n",
       "      <td>1.206208</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "       L      N          t      s         T\n",
       "0  0.247  10.00  10.442000  0.180  1.044200\n",
       "1  0.253  11.75  11.934750  0.170  1.015723\n",
       "2  0.310   8.00   9.042000  0.220  1.130250\n",
       "3  0.330   8.00   9.649667  0.215  1.206208"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.columns = ['N','t','s','L']\n",
    "df = df.groupby([\"L\"], as_index = False).mean()\n",
    "df['T'] = df.apply(lambda row: row['t']/row['N'], axis=1)\n",
    "df['s'] = df.apply(lambda row: row['s']/100, axis=1)\n",
    "df['L'] = df.apply(lambda row: row['L']/100, axis=1)\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Прискорення вільного падіння ми визначимо за допомогою фізичного та математичного маятників, використовуючи наступні співвідношення. Для визначення g за допомогою математичного маятника: $$g_{math} = {4\\pi^2l \\over T^2}$$  \n",
    ",де $l$ - довжина нитки  \n",
    "Для визначення g за допомогою фізичного маятника: $$g_{physics} = {4\\pi^2L \\over T^2}$$  \n",
    ",де $L = {J\\over ms}$ - приведена довжина фізичного маятника($J$ - момент інерції, $m$ - масса, $s$ - довжина від центру мас до осі обертання\n",
    "Якщо період коливань фізичного та математичного маятника дорівнюють один одному, то $L = l$.  \n",
    "Отже виміряємо $l$, $N$ - кількість коливань, $t$ - час, за який ці коливання було здійсненно та за допомогою методу найменших квадратів апроксимуємо лінійною функцією $L(T^2) = kT^2 + b$ залежність $L$ від $T^2$: $$L = l = {t^2\\over 4\\pi^2N^2}g = {T^2\\over 4\\pi^2}g$$\n",
    "Таким чином отриманий коефіцієнт $k$ дорівнює: $$k = {g \\over 4\\pi^2}$$\n",
    "Отже, виразимо $g$ через $k$: $$g = {4k\\pi^2}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "g = 8.195768740997073\n"
     ]
    }
   ],
   "source": [
    "x = df['T'].apply(lambda x: x**2)\n",
    "y = df['L']\n",
    "basis = np.vstack((x,np.ones(4))).T\n",
    "koef = scipy.linalg.lstsq(basis, y)[0]\n",
    "print(\"g = \" + str(koef[0]*4*np.pi**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Отже коефіцієнт вільного падіння $g$, отриманий за результатами експериментів з фізичним маятником: $8.2{м \\over с^2}$.  \n",
    "Візуалізуємо результат, побудувавши теоретичну залежність апроксимовану функцію на відрізку $T^2 = [1, 1.5]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "xnew = np.arange(1, 1.5, 0.01)\n",
    "yideal = 9.81 / (4*np.pi**2) * xnew\n",
    "ynew = koef[0] * xnew + koef[1]\n",
    "plt.figure(figsize = (10,5))\n",
    "plt.title(\"Приведена довжина($L$) в залежності від квадрату періоду $(T^2)$\")\n",
    "plt.xlabel(\"$T^2 (с^2)$\")\n",
    "plt.rc('font', size=15)\n",
    "plt.ylabel(\"$L (м)$\")\n",
    "plt.grid();\n",
    "\n",
    "plt.plot(x, y, 'o', label = \"Результати замірів\")\n",
    "plt.plot(xnew, ynew, '-', label = \"Апроксімована залежність\")\n",
    "plt.plot(xnew, yideal, '--', label = \"Теоретична залежність\");\n",
    "plt.legend(loc=\"best\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для перевірки отриманих результатів, порівняємо значення прискорення вільного падіння($g$) з експерименту та довідника.\n",
    "Для обчислення похибки використаємо систематичну абсолютну похибку, яка отримана з наступних міркувань:\n",
    "$$g = (4\\pi^2{L\\over T^2})$$\n",
    "Пролагорифмуємо цей вираз та отримаємо:\n",
    "$$\\ln g = \\ln(4\\pi^2{L\\over T^2}) = \\ln(4\\pi^2) + \\ln L + \\ln N^2 - \\ln t^2$$\n",
    "Обраховуємо дифференціал:\n",
    "$$\\partial \\ln g = \\partial \\ln (4 * \\pi^2) + \\partial \\ln L + \\partial \\ln N^2 - \\partial \\ln t^2 = \\partial \\ln L + \\partial \\ln N^2 + \\partial \\ln t^2$$  \n",
    "$${\\partial g \\over g} = {\\partial L \\over L} + {2\\partial N \\over N} + {2\\partial t \\over t}$$  \n",
    "Замінюючи дифференціали на значення похибки вимірів($\\Delta t = 0.001(с), \\Delta L = 0.01(м), \\Delta N = 0$) та значення вимірів на середнє, маємо:\n",
    "$$\\Delta g = g({\\Delta L \\over \\overline L} + {2\\Delta t \\over \\overline t})$$\n",
    "Та відносне відхилення $\\delta$. Для $g$ - це: $$\\delta = {|g_{експеримент} - g_{теоретичне}|\\over g_{теоретичне}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def delta(time, lenght, deltaTime, deltaLenght):\n",
    "    return koef[0] * 4*np.pi**2 * (2/time.mean()*deltaTime + 1/lenght.mean()*deltaLenght)\n",
    "#def meanSquaredDelta(time, lenght, deltaTime, deltaLenght):\n",
    "#    return koef[0] * 4 * np.pi**2 * np.sqrt((2/time.mean()*deltaTime)**2 + (1/lenght.mean()*deltaLenght)**2);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "relError = 0.16454956768633308\n",
      "delta = 0.2891673433105003\n"
     ]
    }
   ],
   "source": [
    "delta = delta(df['t'],df['L'], 0.001, 0.01)\n",
    "#msDelta = meanSquaredDelta(df['t'], df['L'], 0.001, 0.01)\n",
    "relError = abs(koef[0] * 4*np.pi**2 - 9.81) / 9.81\n",
    "print(\"relError = \" + str(relError))\n",
    "print(\"delta = \" + str(delta))\n",
    "#print(\"msDelta = \" + str(msDelta))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Отримаємо: \n",
    "- абсолютна похибка $\\Delta g \\approx 0.3$\n",
    "- відносна похибка отриманого та теоретичного значення $g$: $\\delta \\approx 0.16$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Висновок\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Отже, за допомогою синхронізованих(мають однаковий період коливань) математичного і фізичного маятника ми отримали значення прискорення вільного падіння $g = 8.2 \\pm 0.3 {м \\over с^2}$. Воно істотно(на $\\approx 16\\%$) відрізняється від теоретичного, що можливо пояснити різницею у періодах математичного та фізичного маятників, що спричинена неточністю вимірів та людським фактором."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "PhysicsLabs",
   "language": "python",
   "name": "physicslabs"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}