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 },
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Chapter 7: Waves and Oscillations"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.1, Page 7.22"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import pi, sin, sqrt\n",
      "\n",
      "# Given \n",
      "E = 1.024e-3 # total energy of particle in J\n",
      "T = 2 * pi # time period of S.H.M. in sec\n",
      "x = 0.08 * sqrt(2) # distance of partile in meter\n",
      "t = pi / 4 # time in second\n",
      "\n",
      "#Calculations\n",
      "A = x / sin((2 * pi * t) / T)\n",
      "M = (E * T**2) / (2 * pi**2 * A**2)\n",
      "\n",
      "#Result\n",
      "print \"Amplitude = %.2f meter\\nMass of particle = %.f g\"%(A,M/1e-3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Amplitude = 0.16 meter\n",
        "Mass of particle = 80 g\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.2, Page 7.22"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import pi\n",
      "\n",
      "# Given \n",
      "A = 0.05 # amplitude in meter\n",
      "T = 10 # time period of S.H.M. in sec\n",
      "\n",
      "#Calculations\n",
      "v = (A * 2 * pi) / T\n",
      "\n",
      "#Result\n",
      "print \"Maximum amplitude of velocity = %.4f meter/sec\"%v"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Maximum amplitude of velocity = 0.0314 meter/sec\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.3, Page 7.23"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import pi, sqrt\n",
      "\n",
      "# Given \n",
      "E = 9 # total energy of particle in J\n",
      "U = 5 # potential energy in J\n",
      "A = 1 # amplitude in meter\n",
      "m = 2. # mass of harmonic oscillator in kg\n",
      "\n",
      "#Calculations\n",
      "kE = E - U# calculation for kinetic energy\n",
      "k = (2 * kE) / A**2# calculation for force constant\n",
      "T = (2 * pi) * sqrt(m / k)# calculation for time period\n",
      "\n",
      "#Result\n",
      "print \"Force constant = %.f J/m\\nTime period = %.2f sec\"%(k,T)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Force constant = 8 J/m\n",
        "Time period = 3.14 sec\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.4, Page 7.23"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import asin, sin, pi\n",
      "\n",
      "# Given \n",
      "A = 0.06 # amplitude in meter\n",
      "T = 6 # time period of S.H.M. in sec\n",
      "x = 0.03 # position of particle in meter\n",
      "\n",
      "#Calculations\n",
      "delta = asin(1) # by the formula x=Asin(wt+delta) and (at t = 0,x=A) \n",
      "t = x / (A * sin(((2 * pi) / T) + delta))\n",
      "\n",
      "#Result\n",
      "print \"Time taken by the particle = %.f sec\"%t"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Time taken by the particle = 1 sec\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.5, Page 7.24"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import pi\n",
      "\n",
      "# Given \n",
      "A = 0.05# amplitude in meter\n",
      "T = 10 * pi # time period of s.h.m. in sec\n",
      "\n",
      "#Calculations\n",
      "v = A * (2 * pi / T)\n",
      "a = A * (2 * pi / T)**2\n",
      "\n",
      "#Result\n",
      "print \"Maximum velocity = %.e meter/sec\\nacceleration = %.e m/sec^2\"%(v,a)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Maximum velocity = 1e-02 meter/sec\n",
        "acceleration = 2e-03 m/sec^2\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.6, Page 7.24"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import pi\n",
      "\n",
      "# Given \n",
      "A = 0.06# amplitude in meter\n",
      "T = 10 * pi # time period of s.h.m. in sec\n",
      "\n",
      "#Calculation\n",
      "v = A * (2 * pi / T)\n",
      "\n",
      "#Result\n",
      "print \"Maximum velocity = %.1e meter/sec\"%v"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Maximum velocity = 1.2e-02 meter/sec\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.7, Page 7.24"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import sqrt, pi\n",
      "\n",
      "# Given \n",
      "k = 16 # stiffness constant of spring n/m\n",
      "m = 1 # mass of particle in kg\n",
      "\n",
      "#Calculations\n",
      "n = sqrt(k / m) / (2 * pi)\n",
      "\n",
      "#Result\n",
      "print \"natural frequency = %.2f Hz\"%n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "natural frequency = 0.64 Hz\n"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.8, Page 7.25"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import sqrt, pi\n",
      "\n",
      "# Given \n",
      "l = 1 # length of pendulum in meter\n",
      "m = 2 # mass of particle in kg\n",
      "g = 9.8 # acceleration due to gravity in m/sec^2\n",
      "\n",
      "#Calculation\n",
      "T = 2 * pi * sqrt(l / g)\n",
      "\n",
      "#Result\n",
      "print \"The time period of pendulum = %.f sec\"%T"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The time period of pendulum = 2 sec\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.9, Page 7.25"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import sqrt, pi\n",
      "\n",
      "# Given \n",
      "m = 100. # mass of particle in gm\n",
      "\n",
      "#Calculation\n",
      "n = (1 / (2 * pi)) * sqrt(10 / m) # by using given formula \n",
      "\n",
      "#Result\n",
      "print \"Frequency  = %.2f Hz\"%n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Frequency  = 0.05 Hz\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.10, Page 7.25"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import sqrt, pi\n",
      "\n",
      "# Given \n",
      "f = 3 # acceleration of pendulum in m/sec^2\n",
      "l = 1 # length of pendulum in meter\n",
      "g = 9.8 # acceleration due to gravity in m/sec^2\n",
      "\n",
      "#calculatiom\n",
      "T = 2 * pi * sqrt(l / (g + f))\n",
      "\n",
      "#Result\n",
      "print \"Time period of pendulum = %.2f sec\"%T"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Time period of pendulum = 1.76 sec\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.11, Page 7.26"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import sqrt, pi\n",
      "\n",
      "# Given \n",
      "x = 0.3 # stretch in spring in meter\n",
      "m1 = 6 # mass of first body in kg\n",
      "m2 = 1 # mass of second body in kg\n",
      "g = 9.8 #  gravitational acceleration of earth in m/sec^2\n",
      "\n",
      "#Calculations\n",
      "k = (m1 * g) / x\n",
      "T = (2 * pi) * sqrt(m2 / k)\n",
      "\n",
      "#Result\n",
      "print \"Time period of motion = %.2f sec \"%T"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Time period of motion = 0.45 sec \n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.12, Page 7.26"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import sqrt, pi\n",
      "\n",
      "# Given \n",
      "x = 0.1 # compression in spring in m\n",
      "F = 10 # restoring force in N\n",
      "m = 4 # mass of body in kg\n",
      "g = 9.8 # acceleration due to gravity in m/sec^2\n",
      "\n",
      "#Calculations\n",
      "k = F / x\n",
      "F_ = m * g\n",
      "x_ = F_ / k\n",
      "T = (2 * pi) * sqrt(m / k)\n",
      "\n",
      "#Result\n",
      "print \"Time period of motion = %.2f sec \\nCompression of the spring due to the weight of the body = %.3f m \"%(T,x_)\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Time period of motion = 1.26 sec \n",
        "Compression of the spring due to the weight of the body = 0.392 m \n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.13, Page 7.26"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import exp\n",
      "\n",
      "# Given \n",
      "t = 50. # relaxation time in sec\n",
      "r = 1 / exp(1) # falls in amplitude and energy\n",
      "\n",
      "#Calculations\n",
      "s = 1 / (2 * t)\n",
      "T = 1 / s # by using formula A=A_exp(-st) and using r=A/A_\n",
      "\n",
      "#Result\n",
      "print \"Time = %.f sec\"%T\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Time = 100 sec\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Example 7.14, Page 7.27"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from math import pi, exp\n",
      "\n",
      "# Given \n",
      "n = 260 # frequency in Hz\n",
      "Q = 2000 # quality factor\n",
      "r = 1 / (exp(1)**2) # decrease in amplitude \n",
      "\n",
      "#Calculations\n",
      "tou = Q / (2 * pi * n)\n",
      "t = 2 * tou # by using formula A=A_exp(-st) and using r=A/A_\n",
      "\n",
      "#Result\n",
      "print \"Time = %.3f sec\"%t\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Time = 2.449 sec\n"
       ]
      }
     ],
     "prompt_number": 17
    }
   ],
   "metadata": {}
  }
 ]
}