{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Universidade Federal do Rio Grande do Sul (UFRGS)   \n",
    "Programa de Pós-Graduação em Engenharia Civil (PPGEC)   \n",
    "\n",
    "# PEC00025: Introduction to Vibration Theory\n",
    "\n",
    "\n",
    "### Class 09 - Test P1: time and frequency domain analysis of sdof systems\n",
    "\n",
    "[P1:2019](#P1_2019) - [Question 1](#P1_2019_1), \n",
    "[Question 2](#P1_2019_2), \n",
    "[Question 3](#P1_2019_3), \n",
    "[Question 4](#P1_2019_4).\n",
    "\n",
    "---\n",
    "_Prof. Marcelo M. Rocha, Dr.techn._ [(ORCID)](https://orcid.org/0000-0001-5640-1020)  \n",
    "_Porto Alegre, RS, Brazil_ \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importing Python modules required for this notebook\n",
    "# (this cell must be executed with \"shift+enter\" before any other Python cell)\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from   MRPy import MRPy\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## P1:2019 <a name=\"P1_2019\"></a> \n",
    "\n",
    "_Note: this test is to be solved with the aid of a scientific calculator, which must be able to solve eigenproblems,\n",
    "linear systems, and integrals. The total available time for solving the test is 2h (two hours). The student is allowed\n",
    "to prepare am A4 sheet of paper (two sides) with informations to be consulted during the test._\n",
    "\n",
    "### Question 1 (2 points)  <a name=\"P1_2019_1\"></a> \n",
    "\n",
    "A tower is modelled as a single degree of freedom system with effective mass $m = 50000$kg. \n",
    "Figure 1 presents a sample record for its free vibration response.  \n",
    "\n",
    "1. Estimate the natural vibration frequency, $f_{\\rm n}$, the effective damping ratio, $\\zeta$, and the system stiffness, $k$, from the given record. \n",
    "\n",
    "2. What is the peak displacement response for an initial velocity, $v_0 = 2$m/s?  \n",
    "\n",
    "3. What are the peak velocity and the peak acceleration corresponding to this \n",
    "    peak displacement?\n",
    "\n",
    "<img src=\"resources/tests/P1_2019_fig1.png\" alt=\"Question 1\" width=\"640px\"/>\n",
    "\n",
    "_Obs.: this first question provides the system parameters that shall be used in the following question._  \n",
    "\n",
    "**Answer:** System properties can be estimated from record graphic inspection:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Natural vibration frequency:  1.00 Hz  \n",
      "Ratio of critical damping:    2.56 %   \n",
      "System stiffness:             1974 kN/m\n"
     ]
    }
   ],
   "source": [
    "m  =  50000.                         # given system effective mass\n",
    "\n",
    "fn =  10/10                          # 10 cycles in 10 seconds\n",
    "zt =  np.log(1.5/0.3)/(2*np.pi*10)   # logarithmic decay in 10 cycles\n",
    "k  =  m*(2*np.pi*fn)**2              # stiffness from frequency equation\n",
    "\n",
    "print('Natural vibration frequency: {0:5.2f} Hz  '.format(fn))\n",
    "print('Ratio of critical damping:   {0:5.2f} %   '.format(100*zt))\n",
    "print('System stiffness:            {0:5.0f} kN/m'.format(k/1000))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The peak values of kinematic parameters are calculated from the free vibration formula:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Peak displacement:   0.32 m    \n",
      "Peak velocity:       2.00 m/s  \n",
      "Peak acceleration:  12.56 m/s^2\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u0 =  0.                      # given initial displacement\n",
    "v0 =  2.                      # given initial velocity \n",
    "\n",
    "wn =  2*np.pi*fn              # undamped natural frequency\n",
    "wD =  wn*np.sqrt(1 - zt*zt)   # damped natural frequency\n",
    "\n",
    "up =  np.sqrt(u0**2 + ((v0 + 2*zt*wn*u0)/wD)**2)\n",
    "vp =  wD*up\n",
    "ap = (wD**2)*up\n",
    "\n",
    "print('Peak displacement: {0:6.2f} m    '.format(up))\n",
    "print('Peak velocity:     {0:6.2f} m/s  '.format(vp))\n",
    "print('Peak acceleration: {0:6.2f} m/s^2'.format(ap))\n",
    "\n",
    "F  = MRPy.zeros(1, 16384, Td=128)\n",
    "u  = F.sdof_Duhamel(fn, zt, u0, v0)\n",
    "v  = u.differentiate()\n",
    "a  = v.differentiate()\n",
    "\n",
    "f1 = u.plot_time(1, figsize=(8,2), axis_t=(0, 8, -0.5, 0.5))\n",
    "f2 = v.plot_time(2, figsize=(8,2), axis_t=(0, 8, -2.5, 2.5))\n",
    "f3 = a.plot_time(3, figsize=(8,2), axis_t=(0, 8, -16., 16.))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 2 (2 points) <a name=\"P1_2019_2\"></a> \n",
    "\n",
    "The system is now subjected to a triagular impulsive load, $F(t)$, as depicted in figure 2. \n",
    "\n",
    "1. Estimate the peak displacement considering \n",
    "   $F_0 = 50$kN, with $t_0 = 1$s and $t_{\\rm d} = 0.25$s. \n",
    "2. Estimate the time instant where this peak displacement occurs. \n",
    "\n",
    "<img src=\"resources/tests/P1_2019_fig2.png\" alt=\"Question 2\" width=\"320px\"/>  \n",
    "\n",
    "**Answer:** The load has short duration ($t_{\\rm d} < T_{\\rm n}/4$) and can be converted \n",
    "into an equivalent initial velocity.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Equivalent initial velocity:  0.125 m/s\n",
      "Peak displacement:            0.020 m  \n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "I0 =  250000*0.05/2   # impulse by short duration load\n",
    "v0 =  I0/m           # equivalent initial velocity \n",
    "u0 =  0.             # no initial displacement given\n",
    "\n",
    "up =  np.sqrt(u0**2 + ((v0 + 2*zt*wn*u0)/wD)**2)\n",
    "\n",
    "print('Equivalent initial velocity: {0:6.3f} m/s'.format(v0))\n",
    "print('Peak displacement:           {0:6.3f} m  '.format(up))\n",
    "\n",
    "F  = MRPy.zeros(1, 16384, Td=128)\n",
    "u  = F.sdof_Duhamel(fn, zt, u0, v0)\n",
    "v  = u.differentiate()\n",
    "\n",
    "f3 = u.plot_time(3, figsize=(8,2), axis_t=(0, 8, -0.05, 0.05))\n",
    "f4 = v.plot_time(4, figsize=(8,2), axis_t=(0, 8, -0.20, 0.20))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The response to a short impulse is a sine function. Hence, the displacement peak will\n",
    "occur approximately $T_{\\rm n}/4 = 0.25$s after the impulse onset, what means at $t = 1.25$s.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 3 (3 points) <a name=\"P1_2019_3\"></a> \n",
    "\n",
    "The system is then subjected to a transiente load provided as a time series, \n",
    "$F_i = F(t_i) = F(i\\Delta t)$, as given in figure 3 below with load units \\[kN\\]. \n",
    "\n",
    "1. Estimate the peak displacement by regarding the system response as a superposition of four discrete impulses. \n",
    "2. Estimate the time instant where this peak displacement occurs.\n",
    "\n",
    "<img src=\"resources/tests/P1_2019_fig3.png\" alt=\"Question 3\" width=\"320px\"/>  \n",
    "\n",
    "**Answer:** This loading function is too long to be considered as a single impulse.\n",
    "It will be considered a series of impulses, as in the concept of Duhamel integral.\n",
    "The system response for an impulse at $t_i$ can be calculated as:\n",
    "\n",
    "$$ u_i(t) = \\frac{v_{0,i}}{\\omega_{\\rm D}} \\; \n",
    "            e^{-\\zeta \\omega_{\\rm n} (t - t_i)} \\; \n",
    "            \\sin \\omega_{\\rm D} (t - t_i)$$\n",
    "\n",
    "with:\n",
    "\n",
    "$$ v_{0,i} = \\frac{I_i}{m}$$\n",
    "\n",
    "where the discrete impulse, $I_i$, may be approximated by:\n",
    "\n",
    "$$ I_i \\approx \\Delta t \\, F_i $$\n",
    "\n",
    "The total response is the sum of these responses, where the starting times must be considered.\n",
    "Firstly we input the loading function as a ```numpy``` vector.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZmZmdpk6dWjzhj5O7M2dLLs+uPEhaClzbtiwdahX/31E5OTlkZCTP0YATqXfX/nymb8plxsZD7DkEDSulcE7jNLrVTaNMaulr9HpvE1cy1QrJVW9Ytfbt23fRkT7GDr3Bm1lf4FGgl7t/HV1Xz923mFkt4B1gtLvPLOr1srOzfdWqVcWS/Xjs2X+IO15ZzitLt9Atqzp/vbw9dauUD+S1ZsyYQZ8+fQJ57tKoOOrdfyiPV5d+wYTZG1j11R5qZpThim6NubJ741L1NUW9t4krmWqF5Ko3rFrN7IgNPtSz6M3sFOAJoP/3zR3A3bdE/91mZv8AugJFNvgwfbR5F6MnL2HTzn38/KwWjDqjmc7iLmXKpadyWZdGXNq5IXPWfs2EOesZO30Nf5vxGRe2r8c1PZvQup6+ZiciiSG0Bm9mjYCXgSHuvrrA+opAirvvid4/B7g7pJhFys93npy9nvve/pTMjLJMGXkqXbOqhx1LjsLM6NW8Jr2a12Td9hwmfrCBFxZu5sVFm+l+UnWG9czizJNr6w80EYlrQX5NbjLQB6hpZpuBu4B0AHd/DLgTqAE8Gj3h6fuvw9UG/hFdlwZMcve3gsp5InbkHOAXU5fx/urtnNOqNvcNPIWqFcqEHUuOwUmZGdw9oA2/ODubKQs28vQHGxj57CIa16jAtb2yuKJbY1LU6EUkDgV5Fv2gIrZfC1xbyPp1QLugchWX2Wt28POpS9n93SHuGdCaK7s31pnZcaxKhXSuO70pw3tl8faKr3hy9jrueHUFq7/K4e4BrfXeikjc0Ux2x+hQXj4PvLOax97/jKaZGTwzrCsn160cdiwpJmmpKZx/Sl3Oa1uHe9/8lMdnriMt1bjzglZq8iISV9Tgj8Gmnfu4ccoSlmzcxeVdGnLnj1pRoYz+EyYiM2NM/5YcynMmzFlPmdQUxvRvqSYvInGjyO5kZqcCVwK9gbrAd8By4J/Ac+6+O9CEpcQbH23h9pc+BuChQR34Ubt6ISeSoJkZd1xwMofy8nl85jrSU1P4xTkt1ORFJC4ctcGb2ZvAFuBV4HfANqAc0ALoC7xqZg+4+2tBBw3Ldwfz+M3rK5iyYBPtG1bloUEdaFi9QtixpISYGb+5sDW5+fk8/N5a0lNTuOms5mHHEhEpUlF78EMKmQ8+B1gcvf3ZzGoGkqwU+HTrt4yatITPtudwfZ+m3Hx2C9JTU8KOJSUsJcX43UVtOZTn/OXd1aSlGjf0bRZ2LBGRozpqg4/lYi/xfkGYwrg7z83byD1vrKRK+XSeGdaV3s0zw44lIUpJMf7441PIzcvn/rdXUSY1hRGnnRR2LBGRIyrqEP16IvPB/2dVgWV396ZBBQvLrn0Hue2lj3h7xVec3iKTP1/ajpoZpWcaUwlPaorxp0vacSjf+d20T0hLNa7pmRV2LBGRQhV1iP7w+W1TgEuBW4AlgSQK0YINO7lp8hK27TnAL887meG9sjTJifyXtNQU/npZe3Lz8vnN6ytJS01hSPfGYccSEfmBo36g7O5fR+eI/wa4AHgPOBU4391/XAL5SkRevjP23TVc9viHpKel8NL1PRhx2klq7lKo9NQUHhrUkbNOrsUdryzn+QUbw44kIvIDRR2iTweGAT8HZgMD3P2zkghWUr7c/R0/m7KUeet3MqB9PX57URsqlUsPO5aUcmXSUnjkio6MfGYRY17+mNSUFAZ2ahB2LBGR/yjqEP16IBf4K7ARaGdm/5lG1t1fDjBb4N5d+RW3vriMA7n5/OmSdvy4Y319x1liVjYtlceHdOLapxdy64vLSE81BrSvH3YsERGg6Ab/LpGT6trxw/nhncjV4OLO/kN53Pvmp0z8YAOt6lbmocEdaJqZEXYsiUPl0lMZf1Vnrpk4n5unLiMtJTLVrYhI2Ir6mtzQEspRYj7bnsPoSUtY+eW3DO3RhNvPa0nZtNSwY0kcK18mlSev7sLQp+Zz05QlpKUa57auE3YsEUlyRz3JzsyuNLMjjjGzpmbWq/hjFT9354WFm/jRQ7P5cvd3PHFVZ359YWs1dykWFcum8dQ1XWnboAqjJi1m+idfhR1JRJJcUYfoawBLzGwRsAjYTmSq2mbA6cAOYEygCYvBnv2H+NUry3l16Ra6ZVVn7OUdqFOlXNixJMFklE1j4jVdGfLkPK5/bjHjr+7M6S00QZKIhKOor8mNBToCk4FM4Mzo8hdEprH9sbuvCTzlCVi2aRcXPDSb15dt4eazWzBpRHc1dwnM9zMfNquVwchnFjJnbcJN9CgicaLIq8m5ex7wTvQWN/LznSdmr+O+t1ZRq1JZnr/uVLo0qR52LEkCVSuU4blruzF4/FyGP72Aidd0pftJNcKOJSJJJiGvnLJ9zwGGTlzA76d9ypkn12LaTb3V3KVEVa8YafINqlVg2MQFLNywM+xIIpJkAm3wZjbBzLaZ2fIjbDcze9DM1prZR2bWscC2q81sTfR2dayvOWvNdvqPncXcdV9zz0VteOzKTlStUKY4yhE5JjUzyjLp2m7UqVyOoU8tYMnGb8KOJCJJJOg9+IlAv6Ns7w80j95GAn8DMLPqwF1AN6ArcJeZVSvqxb7Z71w1YT5VK6Tz2qieDOneWBPXSKhqVS7HpBHdqZFRhqsmzOfjzbvDjiQiSSKmBm9mtc3sSTN7M7rcysyGF/U4d58JHO3Y5ADgGY+YC1Q1s7rAucA77r7T3b8h8vn/0f5QAGD3QefyLg15fVQvWtapHEtpIoGrUyXS5KuUT+fKJ+exYouavIgEz9y96EGRxv4U8Et3b2dmacASd28bw2ObAG+4e5tCtr0B3Ovus6PL04HbgD5AOXf/bXT9HcB37v6nQp5jJJG9f6rWqtfpH8//vch6EkFOTg4ZGckz+14i1Lt9Xz5/mL+fg3nOmK7laVCp8L+vE6HWY5FM9SZTrZBc9YZVa9++fRe5++FXfgViOIs+qqa7TzWz2wHcPdfM8oohW2HHz/0o63+40n0cMA4gOzvb+/TpUwyxSr8ZM2aQLLVC4tTbpeteLhv3IX9dlseUkV1oVqvSD8YkSq2xSqZ6k6lWSK56S2OtsX4Gv9fMahBtsmbWHSiO44ybgYYFlhsAW46yXiSuNalZkUkjumNmDBo/j3Xbc8KOJCIJKtYGfzPwGtDUzOYAzwCji+H1XwOuip5N3x3Y7e5fAm8D55hZtejJdedE14nEvaaZGUy6thv5+c7g8fP4/Ou9YUcSkQQUU4N398VEpqbtAVwHtHb3j4p6nJlNBj4Ess1ss5kNN7OfmNlPokOmAeuAtcB44KfR19sJ3AMsiN7ujq4TSQjNa1fi7yO6cSA3j8Hj57Fp576wI4lIgonpM3gzuwH4u7uviC5XM7NB7v7o0R7n7oOK2O7ADUfYNgGYEEs+kXjUsk5lnh0emfFu8BNzeX7kqdSrWj7sWCKSIGI9RD/C3Xd9vxD96tqIYCKJJI829avw7PBu7Np7iMHj57J19/6wI4lIgoi1wadYgRljzCwV0PRwIsWgXcOqPD28K9v3HGDwE3PZdSA/7EgikgBibfD/Aqaa2ZlmdgaRq8u9FVwskeTSsVE1Jg7rype79nPfgv18nXMg7EgiEudibfD/D5gOXE/kM/Pp0XUiUky6NKnOhKFd2LHPueKJeXyz92DYkUQkjhXZ4KOH459x98fcfWD0GvCPRy8jKyLF6NSmNbipYznW7djLlU/OY/e+Q2FHEpE4VWSDjzbyTDPTZ+4iJaB1zVTGDenEmq9yuGrCPL7dryYvIscu1kP0G4A5ZnaHmd38/S3AXCJJrU92LR69oiMrtnzL0AnzyTmQG3YkEYkzsTb4LcAb0fGVCtxEJCBntarNw4M7sGzzboY9tYB9B9XkRSR2MU104+6/ATCzSpFF1wTaIiWgX5u6jL3cuXHyEoZPXMiEoV0oXyY17FgiEgdivR58GzNbAiwHVpjZIjNrHWw0EQG44JR6PHBpe+au/5qRzy5k/yGd3yoiRYv1EP044GZ3b+zujYFfEJk7XkRKwEUd6nPfj09h1podXP/cIg7kqsmLyNHF2uAruvt73y+4+wygYiCJRKRQl3RuyB/+py3vrdrODX9fwsFczXgnIkcWa4NfFz2Dvkn09itgfZDBROSHBnVtxD0DWvPuJ19x4+QlHMpTkxeRwsXa4IcBmcDL0VtN4JqgQonIkQ05tQl3XNCKt1Zs5eapy8hVkxeRQhz1LHoze9bdhwBXufuNJZRJRIowvFcWuXn5/OHNT0lPMe6/pB2pKVb0A0UkaRT1NblOZtYYGGZmzwD/9RvE3XcGlkxEjuq605tyKC+fP/1rNakpxh9/fAopavIiElVUg3+MyFXjTgIW8d8N3qPrRSQko85ozqE8Z+z0NaSlpvD7i9tQ4MrOIpLEjtrg3f1B4EEz+5u7X19CmUTkGPzsrOYcysvn0RmfUSbV+PWFrdXkRSTmmeyOq7mbWT9gLJAKPOHu9x62/S9A3+hiBaCWu1eNbssDPo5u2+juFx5PBpFEZ2bcem42h/LyGT9rPWmpKfzq/JPV5EWSXEwN/nhELzP7CHA2sBlYYGavufvK78e4+88LjB8NdCjwFN+5e/ug8okkEjPjf887mUN5zpOz15OWaozp11JNXiSJBdbgga7AWndfB2BmU4ABwMojjB8E3BVgHpGEZmbc9aNW5Obn8/j76yibmsLN52SHHUtEQmLuHswTmw0E+rn7tdHlIUA3dx9VyNjGwFygQfT685hZLrAUyAXudfdXjvA6I4GRAJmZmZ2mTp0aRDmlTk5ODhkZGWHHKDHJVO+J1prvzsQVB5m5OZeLm6UzoFmZYkxX/PTeJq5kqjesWvv27bvI3TsXti3IPfjCjg0e6a+Jy4EXv2/uUY3cfYuZnQT828w+dvfPfvCE7uOIzJVPdna29+nT5wRjx4cZM2aQLLVCctVbHLX2Od255cVlvLz4C1o0a8r1fZoWT7gA6L1NXMlUb2msNcgGvxloWGC5AZHryhfmcuCGgivcfUv033VmNoPI5/M/aPAi8kMpKcb9A9uRm+f88a1PSU81ru2tb7WKJJMgG/wCoLmZZQFfEGnigw8fZGbZQDXgwwLrqgH73P2AmdUEegL3BZhVJOGkphgPXNqO3Px8fvvPT0hPTeHqHk3CjiUiJSSwBu/uuWY2CnibyNfkJrj7CjO7G1jo7q9Fhw4Cpvh/nwxwMvC4meUTmS//3oJn34tIbNJSUxh7eQcO5S3mrtdWkJZqXNGtcdixRKQEBLkHj7tPA6Ydtu7Ow5Z/XcjjPgDaBplNJFmkp6bw8OAOXP/cYn75j+Wkp6RwaZeGRT9QROJarFeTE5E4VjYtlUev6MhpLTK57eWPeHnx5rAjiUjA1OBFkkS59FTGDenEqSfV4JYXlvHasiOd8yoiiUANXiSJlEtP5YmrO9O5SXV+/vxSpn38ZdiRRCQgavAiSaZCmTQmDO1C+4ZVuXHyEv61YmvYkUQkAGrwIkkoo2waE6/pQpv6Vbhh0mLe+3Rb2JFEpJipwYskqUrl0nl6WFey61TiuucWMXP19rAjiUgxUoMXSWJVyqfz3PBuNM3MYMQzC/lg7Y6wI4lIMVGDF0lyVSuU4bnhXWlcowLDn17IvHVfhx1JRIqBGryIUCOjLH+/tjv1qpbjmokLWPT5zrAjicgJUoMXEQAyK5Vl8oju1K5cjqsnLGDppl1hRxKRE6AGLyL/UatyOSaN6Eb1imUY8uQ8ln+xO+xIInKc1OBF5L/UrVKeSSO6UblcOlc+OY+VW74NO5KIHAc1eBH5gQbVKjB5RHfKp6dy5ZPzWLV1T9iRROQYqcGLSKEa1ajApBHdSUsxrnhiLmu35YQdSUSOgRq8iBxRVs2KTBrRHYDB4+eyfsfekBOJSKzU4EXkqJrVymDSiO7k5juDx89l49f7wo4kIjFQgxeRIrWoXYnnhnfju0N5DBo/l83fqMmLlHZq8CISk1b1KvPc8G7s2X+IQePn8uXu78KOJCJHEWiDN7N+ZrbKzNaa2ZhCtg81s+1mtjR6u7bAtqvNbE30dnWQOUUkNm3qV+GZ4d3YtfcQg8fP46tv94cdSUSOILAGb2apwCNAf6AVMMjMWhUy9Hl3bx+9PRF9bCip7OMAABHGSURBVHXgLqAb0BW4y8yqBZVVRGLXvmFVJg7rwrZv9zN4/Fy27zkQdiQRKUSQe/BdgbXuvs7dDwJTgAExPvZc4B133+nu3wDvAP0Cyikix6hT4+pMGNqFLbv2c8UTc9mRoyYvUtqYuwfzxGYDgX7ufm10eQjQzd1HFRgzFPgDsB1YDfzc3TeZ2S1AOXf/bXTcHcB37v6nQl5nJDASIDMzs9PUqVMDqae0ycnJISMjI+wYJSaZ6o2nWld+ncdfFu0nI924rl1ZWlZPPebniKd6T1Qy1QrJVW9Ytfbt23eRu3cubFtagK9rhaw7/K+J14HJ7n7AzH4CPA2cEeNjIyvdxwHjALKzs71Pnz7HHTiezJgxg2SpFZKr3niqtQ/Qu9tuRk9ezH0L9jH6jOaMPqMZaamxHxyMp3pPVDLVCslVb2msNchD9JuBhgWWGwBbCg5w96/d/ftje+OBTrE+VkRKh7YNqvDGjb25qH19xk5fw+Dx89iyS2fYi4QtyAa/AGhuZllmVga4HHit4AAzq1tg8ULgk+j9t4FzzKxa9OS6c6LrRKQUyiibxgOXteeBS9uxfMtu+o+dxb9WbA07lkhSC6zBu3suMIpIY/4EmOruK8zsbjO7MDrsRjNbYWbLgBuBodHH7gTuIfJHwgLg7ug6ESnF/qdjA/55Y28aVi/PyGcXceery9l/KC/sWCJJKcjP4HH3acC0w9bdWeD+7cDtR3jsBGBCkPlEpPhl1azIS9f34L63VvHk7PXMX7+Thwd3oFmtSmFHE0kqmslORIpd2bRU7rigFU8N7cK2PQf40UNzeH7BRoL61o6I/JAavIgEpm/LWrx5U286NKrKbS99zOjJS/h2/6GwY4kkBTV4EQlU7crleHZ4N249N5s3l2/l/AdnsWTjN2HHEkl4avAiErjUFOOGvs2Yel138vPhksc+5G8zPiM/X4fsRYKiBi8iJaZT4+pMu7E3Z7eqzR/f+pSrn5rPrgP5YccSSUhq8CJSoqpUSOfRKzry+4vbMn/9Tu6c8x3vr94ediyRhKMGLyIlzswY3K0Rr4/uRaUyxtUT5vOHaZ9wMFd78yLFRQ1eRELTonYl7jq1PFd0a8TjM9dxyWMf8PnXe8OOJZIQ1OBFJFRlUo3fXdyWv13RkfU79nL+g7N5dekXYccSiXtq8CJSKvRvW5dpN/Umu04lbpqylFtfWMa+g7lhxxKJW2rwIlJqNKhWgedHdmdU32a8uHgzFzw0mxVbdocdSyQuqcGLSKmSlprCLedm8/fh3cjZn8vFj3zAxDnrNc2tyDFSgxeRUqlHs5q8eVNvejWvya9fX8mIZxbxzd6DYccSiRtq8CJSatXIKMuTV3fmjgta8f7qbfQfO4u5674OO5ZIXFCDF5FSzcwY3iuLf/y0J+XLpDJ4/FweeGc1uXn6zrzI0ajBi0hcaFO/Cq+P7sVFHerz4PQ1DB4/jy27vgs7lkippQYvInEjo2waD1zanr9c1o4VW3bTf+ws3l6xNexYIqWSGryIxJ2LOzTgjRt706h6Ba57dhF3vLKc/Yfywo4lUqoE2uDNrJ+ZrTKztWY2ppDtN5vZSjP7yMymm1njAtvyzGxp9PZakDlFJP5k1azIS9f34NpeWTw793MuemQOa7ftCTuWSKkRWIM3s1TgEaA/0AoYZGatDhu2BOjs7qcALwL3Fdj2nbu3j94uDCqniMSvMmkp/OqCVjw1tAvb9xzgRw/N4fkFG/WdeRGC3YPvCqx193XufhCYAgwoOMDd33P3fdHFuUCDAPOISILq27IWb97Um46Nq3LbSx8zevISvt1/KOxYIqEKssHXBzYVWN4cXXckw4E3CyyXM7OFZjbXzC4KIqCIJI5alcvxzLBu3HpuNm8u38r5D85iycZvwo4lEhoL6lCWmV0CnOvu10aXhwBd3X10IWOvBEYBp7v7gei6eu6+xcxOAv4NnOnunxXy2JHASIDMzMxOU6dODaSe0iYnJ4eMjIywY5SYZKo3mWqFYOpd+00ef1t2gF0HnP9pnk7/rHRSzIr1NY6H3tvEFVatffv2XeTunQvblhbg624GGhZYbgBsOXyQmZ0F/JICzR3A3bdE/11nZjOADsAPGry7jwPGAWRnZ3ufPn2Kr4JSbMaMGSRLrZBc9SZTrRBMvX2AS/od4n9f/pgXPv6SrV6FP1/ajlqVyhXr6xwrvbeJqzTWGuQh+gVAczPLMrMywOXAf50Nb2YdgMeBC919W4H11cysbPR+TaAnsDLArCKSYKqUT+fhwR34/cVtmb9+J+eNncX7q7eHHUukxATW4N09l8hh97eBT4Cp7r7CzO42s+/Pir8fyABeOOzrcCcDC81sGfAecK+7q8GLyDExMwZ3a8Tro3tRo2JZrp4wn99P+4SDuZrmVhJfkIfocfdpwLTD1t1Z4P5ZR3jcB0DbILOJSPJoUbsSr47qyT1vrGTczHXMW/c1Dw7qQOMaFcOOJhIYzWQnIkmhXHoqv7u4LX+7oiPrd+zl/Adn8+rSL8KOJRIYNXgRSSr929Zl2k29aVmnEjdNWcotLyxj74HcsGOJFDs1eBFJOg2qVWDKyO6MPqMZLy3ezI8ens2KLbvDjiVSrNTgRSQppaWm8Itzsvn7td3YeyCXix/5gKfmrNc0t5Iw1OBFJKn1aFqTN286jd7Na/Kb11cy4pmF7Nx7MOxYIidMDV5Ekl71imV44urO3HlBK2au3sF5Y2cxd93XYccSOSFq8CIiRL4zP6xXFi//tAfly6QyePxcHnhnNbl5+s68xCc1eBGRAtrUr8Ibo3txcYcGPDh9DYPGz2XLru/CjiVyzNTgRUQOU7FsGn++tB1/vaw9K7d8S/+xs3h7xdawY4kcEzV4EZEjuKhDff55Y28aVa/Adc8u4o5XlrP/UF7YsURiogYvInIUTWpW5KXrezCidxbPzv2cix6Zw9pte8KOJVIkNXgRkSKUSUvhl+e34qlrurB9zwEueGg2U+Zv1HfmpVRTgxcRiVHf7Fq8eVNvOjWuxpiXP2bU5CV8u/9Q2LFECqUGLyJyDGpVLsezw7px67nZvLV8K+eNncXijd+EHUvkB9TgRUSOUUqKcUPfZky97lTc4dLHPuTRGWvJz9cheyk91OBFRI5Tp8bVmHZTb85tXYf73lrFVRPms23P/rBjiQBq8CIiJ6RK+XQeHtyBP/xPWxZ+vpP+f53FjFXbwo4logYvInKizIxBXRvx+qhe1Mwoy9CnFvD7aZ9wMFfT3Ep41OBFRIpJ89qVeHVUT67s3ohxM9cx8LEP2LBjb9ixJEkF2uDNrJ+ZrTKztWY2ppDtZc3s+ej2eWbWpMC226PrV5nZuUHmFBEpLuXSU/ntRW157MqObNixlwsems2rS78IO5YkocAavJmlAo8A/YFWwCAza3XYsOHAN+7eDPgL8MfoY1sBlwOtgX7Ao9HnExGJC/3a1OXNn51GyzqVuGnKUm55YRn7c3WWvZSctACfuyuw1t3XAZjZFGAAsLLAmAHAr6P3XwQeNjOLrp/i7geA9Wa2Nvp8HwaYV0SkWNWvWp4pI7vz4PQ1PPTeWl4xKDvzrbBjlZi8vDxS/3189f7lsvac07pOMSdKLkE2+PrApgLLm4FuRxrj7rlmthuoEV0/97DH1i/sRcxsJDAyunjAzJafePS4UBPYEXaIEpRM9SZTrZBc9SZTrXAC9Z57TzEnCV5Y723jI20IssFbIesOPz51pDGxPDay0n0cMA7AzBa6e+djCRmvkqlWSK56k6lWSK56k6lWSK56S2OtQZ5ktxloWGC5AbDlSGPMLA2oAuyM8bEiIiJyBEE2+AVAczPLMrMyRE6ae+2wMa8BV0fvDwT+7ZHLM70GXB49yz4LaA7MDzCriIhIQgnsEH30M/VRwNtAKjDB3VeY2d3AQnd/DXgSeDZ6Et1OIn8EEB03lcgJebnADe6eF8PLjguillIqmWqF5Ko3mWqF5Ko3mWqF5Kq31NVqup6xiIhI4tFMdiIiIglIDV5ERCQBxV2DP5Hpb+NRDPXebGYrzewjM5tuZkf8TmRpV1StBcYNNDM3s1L1lZRjFUu9ZnZp9P1dYWaTSjpjcYnh57iRmb1nZkuiP8vnhZGzOJjZBDPbdqQ5OSziweh/i4/MrGNJZyxOMdR7RbTOj8zsAzNrV9IZi0tRtRYY18XM8sxsYEllK5S7x82NyMl6nwEnAWWAZUCrw8b8FHgsev9y4Pmwcwdcb1+gQvT+9fFabyy1RsdVAmYSmQipc9i5A35vmwNLgGrR5Vph5w6w1nHA9dH7rYANYec+gXpPAzoCy4+w/TzgTSLzfXQH5oWdOeB6exT4Ge4fz/UWVWt0TCrwb2AaMDDMvPG2B/+f6W/d/SDw/fS3BQ0Ano7efxE4Mzr9bTwqsl53f8/d90UX5xKZMyAexfLeAtwD3AfsL8lwAYil3hHAI+7+DYC7x+tFxmOp1YHK0ftViON5L9x9JpFvBR3JAOAZj5gLVDWzuiWTrvgVVa+7f/D9zzDx/TsqlvcWYDTwEhD6/6/x1uALm/728Cls/2v6W+D76W/jUSz1FjScyJ5BPCqyVjPrADR09zdKMlhAYnlvWwAtzGyOmc01s34llq54xVLrr4ErzWwzkT2f0SUTLRTH+v91Ionn31FFMrP6wMXAY2FngWCnqg3CiUx/G49irsXMrgQ6A6cHmig4R63VzFKIXHFwaEkFClgs720akcP0fYjs9cwyszbuvivgbMUtlloHARPd/c9mdiqR+THauHt+8PFKXCL9joqZmfUl0uB7hZ0lQH8FbnP3vNJw4DjeGvyxTH+7+bDpb+NRTFP2mtlZwC+B0z1yBb54VFStlYA2wIzo/zh1gNfM7EJ3X1hiKYtPrD/Lc939EJGrKq4i0vAXlEzEYhNLrcOJXBoad//QzMoRuXhH6Ic5A5B0U3Gb2SnAE0B/d/867DwB6gxMif6OqgmcZ2a57v5KGGHi7RD9iUx/G4+KrDd62Ppx4MI4/owWiqjV3Xe7e013b+LuTYh8lhevzR1i+1l+hchJlJhZTSKH7NeVaMriEUutG4EzAczsZKAcsL1EU5ac14CromfTdwd2u/uXYYcKipk1Al4Ghrj76rDzBMndswr8jnoR+GlYzR3ibA/eT2D623gUY733AxnAC9G/Gje6+4WhhT5OMdaaMGKs923gHDNbCeQBt8bj3k+Mtf4CGG9mPydyuHpovP5hbmaTiXysUjN6TsFdQDqAuz9G5ByD84C1wD7gmnCSFo8Y6r2TyHlQj0Z/R+V6KbvqWqxiqLVU0VS1IiIiCSjeDtGLiIhIDNTgRUREEpAavIiISAJSgxcREUlAavAiIiIJSA1eJAmZWVUz+2mB5Xpm9mJAr3WRmd15lO1tzWxiEK8tksz0NTmRJGSRyyi/4e5tSuC1PiAyKdGOo4x5Fxjm7huDziOSLLQHL5Kc7gWamtlSM7vfzJp8f41rMxtqZq+Y2etmtt7MRpnZzdFrtc81s+rRcU3N7C0zW2Rms8ys5eEvYmYtgAPfN3czu8TMlpvZMjObWWDo68TxpFQipZEavEhyGgN85u7t3f3WQra3AQYTudTr74B97t4B+BC4KjpmHDDa3TsBtwCPFvI8PYHFBZbvBM5193ZAwRkXFwK9T6AeETlMXE1VKyIl5j133wPsMbPdRPawAT4GTjGzDKAH/zdFMkDZQp6nLv89p/wcYKKZTSUyP/n3tgH1ijG/SNJTgxeRwhS8KmF+geV8Ir83UoBd7t6+iOf5jsgVHQFw95+YWTfgfGCpmbWPzq9fLjpWRIqJDtGLJKc9RC7Be1zc/Vsil7C9BCB6ZbR2hQz9BGj2/YKZNXX3ee5+J7CD/7tsagtg+fHmEZEfUoMXSULRveY50RPe7j/Op7kCGG5my4AVwIBCxswEOtj/Hce/38w+jp7QNxNYFl3fF/jnceYQkULoa3IiEigzGwu87u7vHmF7WeB9oJe755ZoOJEEpj14EQna74EKR9neCBij5i5SvLQHLyIikoC0By8iIpKA1OBFREQSkBq8iIhIAlKDFxERSUBq8CIiIgno/wMCLj+4/DENUAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ti = np.array([0.00, 0.25, 0.50, 0.75, 1.00, 1.25])        # starting times of each impulse\n",
    "Fi = np.array([1.00, 1.50, 1.20, 0.50, 0.00, 0.00])*1000   # force value at the starting time\n",
    "\n",
    "plt.figure(1, figsize=(8, 4), clear=True)\n",
    "plt.plot(ti, Fi/1000)\n",
    "\n",
    "plt.xlim(0, 1.5);   plt.xlabel('time (s)') \n",
    "plt.ylim(0, 2.0);   plt.ylabel('force (N)') \n",
    "\n",
    "plt.grid(True) \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and then we calculate the equivalent initial velocities and superpose:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Dt    = 0.25     # load function time step\n",
    "Ii    = Dt*Fi    # impulse values\n",
    "Ii[0] = Ii[0]/2  # accounts for only half time step\n",
    "v0    = Ii/m     # corresponding initial velocities\n",
    "\n",
    "t  = np.linspace(0, 4, 200)  # time domain discretization\n",
    "u  = np.zeros(t.shape)       # reset total displacement\n",
    "dt = 4/200                   # time domain resolution\n",
    "\n",
    "plt.figure(2, figsize=(8, 4), clear=True)\n",
    "plt.xlim( 0.0, 4.0);   plt.xlabel('time (s)') \n",
    "plt.ylim(-5.0, 2.0);   plt.ylabel('displacement (mm)')\n",
    "plt.grid(True)\n",
    "\n",
    "for i in range(4):\n",
    "    \n",
    "    ui = np.zeros(t.shape)   # reset displacement component\n",
    "    i0 = 1 + int(ti[i]/dt)   # impulse starting point\n",
    "\n",
    "    ui[i0:]  = (v0[i]/wD)*np.exp(-zt*wn*t[:-i0])*np.sin(wD*t[:-i0])\n",
    "    u       +=  ui\n",
    "    \n",
    "    plt.plot(t, 1000*ui)\n",
    "\n",
    "plt.legend(('1', '2', '3', '4'), loc=3)\n",
    "\n",
    "plt.figure(3, figsize=(8, 4), clear=True)\n",
    "plt.plot(t, 1000*u)\n",
    "plt.xlim( 0.0, 2.0);   plt.xlabel('time (s)') \n",
    "plt.ylim(-2.0, 2.0);   plt.ylabel('displacement (mm)') \n",
    "plt.legend(('total',))\n",
    "plt.grid(True)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By observing the first time steps it can be concluded that the maximum displacement is\n",
    "approximately 1.25mm occuring around $t = 0.5$s."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 4 (3 points) <a name=\"P1_2019_4\"></a> \n",
    "\n",
    "The system is finally subjected to an horizontal ground acceleration, $a_{\\rm G}(t)$, given as a power spectral density, $S_{\\rm a_G}(f)$, in units \\[${\\rm g^2/Hz}$\\], $g = 9.81{\\rm m/s^2}$, as shown in figure 4 below. \n",
    "\n",
    "1. Estimate the r.m.s. displacement through a frequency domain analysis. \n",
    "2. Estimate how much of this response is due to system resonance with seismic loading.\n",
    "\n",
    "<img src=\"resources/tests/P1_2019_fig4.png\" alt=\"Question 4\" width=\"320px\"/>\n",
    "\n",
    "**Answer:** The power spectral density of the displacement response is given by\n",
    "\n",
    "$$ S_u(f) = \\left| H(f) \\right|^2 \\; S_{\\rm a_G}(f) $$\n",
    "\n",
    "where we regard that the equilibrium equation has been divided by the system mass and:\n",
    "\n",
    "$$ \\left| H(f) \\right|^2 = \\left\\{ \\omega_{\\rm n}^4 \\left[\n",
    "               (1 - \\beta^2)^2 + (2 \\zeta \\beta)^2\n",
    "               \\right] \\right\\}^{-1} $$ \n",
    "\n",
    "with $\\beta = \\omega / \\omega_{\\rm n} = f/f_{\\rm n}$.\n",
    "\n",
    "To calculate the r.m.s. value of the displacement response, the function $S_u(f)$ must\n",
    "be integrated over the whole frequency domain.\n",
    "The $S_{\\rm a_G}(f)$ is constant within two frequency intervals and this must be taken\n",
    "into account for the integration scheme.\n",
    "\n",
    "Firstly we prepare the discretization of frequency domain and the admittance function:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f   = np.linspace(0, 3, 200)                     # be aware that fn = 1Hz, so f = beta\n",
    "Df  = 3/200                                      # frequency domain resolution\n",
    "Hf2 = 1/((wn**4)*((1 - f**2)**2 + (2*zt*f)**2))  # admittance for unit mass\n",
    "\n",
    "plt.figure(4, figsize=(8, 4), clear=True)\n",
    "plt.semilogy(f, Hf2)\n",
    "plt.xlim( 0.0, 3.0);   plt.xlabel('frequency (Hz)') \n",
    "plt.ylim(1e-5, 1e0);   plt.ylabel('admitance') \n",
    "plt.grid(True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we prepare the discrete spectral density of ground acceleration:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Sa = np.zeros(f.shape)   # reset the spectral density\n",
    "i1 = int(1.2/Df)         # position of the first interval\n",
    "i2 = int(2.0/Df)         # position of the second interval\n",
    "\n",
    "Sa[ 0:i1] = 0.010*(9.81**2)\n",
    "Sa[i1:i2] = 0.015*(9.81**2)\n",
    "\n",
    "plt.figure(5, figsize=(8, 4), clear=True)\n",
    "plt.plot(f, Sa)\n",
    "plt.xlim( 0.0, 3.0);   plt.xlabel('frequency (Hz)') \n",
    "plt.ylim( 0.0, 2.0);   plt.ylabel('Acceleration spectrum') \n",
    "plt.grid(True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and finally we calculate and integrate the spectral density of system response:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Displacement r.m.s:  0.138m\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Su  = Hf2*Sa\n",
    "su2 = np.trapz(Su, dx=Df)\n",
    "\n",
    "plt.figure(6, figsize=(8, 4), clear=True)\n",
    "plt.semilogy(f, Su)\n",
    "plt.xlim( 0.0, 3.0);   plt.xlabel('frequency (Hz)') \n",
    "plt.ylim(1e-5, 1e0);   plt.ylabel('Acceleration spectrum') \n",
    "plt.grid(True)\n",
    "\n",
    "print('Displacement r.m.s: {0:6.3f}m'.format(np.sqrt(su2)))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To know how much of this response is purely ressonant, we neglect the frequency dependent\n",
    "part of the mechanical admittance. In this case the purely static admittance is simply:\n",
    "\n",
    "$$ \\left| H(f) \\right|^2 = \\omega_{\\rm n}^{-4} $$ \n",
    "\n",
    "Hence:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Displacement r.m.s:  0.038m\n"
     ]
    }
   ],
   "source": [
    "Su  = Sa/(wn**4)\n",
    "su2 = np.sum(Su)*Df\n",
    "\n",
    "print('Displacement r.m.s: {0:6.3f}m'.format(np.sqrt(su2)))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This means that due to resonance the system r.m.s. response was raised from 0.038m to 0.138m.\n"
   ]
  }
 ],
 "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": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}