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-{

- "metadata": {

-  "name": "chapter24.ipynb"

- },

- "nbformat": 3,

- "nbformat_minor": 0,

- "worksheets": [

-  {

-   "cells": [

-    {

-     "cell_type": "heading",

-     "level": 1,

-     "metadata": {},

-     "source": [

-      "Chapter 24: Mechanical Vibrations"

-     ]

-    },

-    {

-     "cell_type": "heading",

-     "level": 2,

-     "metadata": {},

-     "source": [

-      "Example 24.24-1,Page No:596"

-     ]

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [

-      "import math\n",

-      "\n",

-      "# Initilization of variables\n",

-      "\n",

-      "f=0.1666666 # oscillations/second\n",

-      "x=8 # cm # distance from the mean position\n",

-      "pi=3.14\n",

-      "\n",

-      "# Calculations\n",

-      "\n",

-      "omega=2*pi*f\n",

-      "\n",

-      "# Amplitude is given by eq'n \n",

-      "r=sqrt((25*x**2)/16) # cm\n",

-      "\n",

-      "# Maximum acceleration is given as,\n",

-      "a_max=(pi/3)**2*10 # cm/s^2\n",

-      "\n",

-      "# Velocity when it is at a dist of 5 cm (assume s=5 cm) is given by\n",

-      "s=5 # cm\n",

-      "v=omega*(r**2-s**2)**0.5 # cm/s\n",

-      "\n",

-      "# Results\n",

-      "\n",

-      "print\"(a) The amplitude of oscillation is \",round(r,2),\"cm\"\n",

-      "print\"(b) The maximum acceleration is \",round(a_max,2),\"cm/s^2\"\n",

-      "print\"(c) The velocity of the particle at 5 cm from mean position  is \",round(v,2),\"cm/s\"\n"

-     ],

-     "language": "python",

-     "metadata": {},

-     "outputs": [

-      {

-       "output_type": "stream",

-       "stream": "stdout",

-       "text": [

-        "(a) The amplitude of oscillation is  10.0 cm\n",

-        "(b) The maximum acceleration is  10.96 cm/s^2\n",

-        "(c) The velocity of the particle at 5 cm from mean position  is  9.06 cm/s\n"

-       ]

-      }

-     ],

-     "prompt_number": 3

-    },

-    {

-     "cell_type": "heading",

-     "level": 2,

-     "metadata": {},

-     "source": [

-      "Example 24.24-2,Page No:597"

-     ]

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [

-      "import math\n",

-      "\n",

-      "# Initilization of variables\n",

-      "\n",

-      "x_1=0.1 # m # assume the distance of the particle from mean position as (x_1 & x_2)\n",

-      "x_2=0.2# m \n",

-      "\n",

-      "# assume velocities as v_1 & v_2\n",

-      "\n",

-      "v_1=1.2 # m/s\n",

-      "v_2=0.8 # m/s\n",

-      "pi=3.14\n",

-      "\n",

-      "# Calculations\n",

-      "\n",

-      "# The amplitude of oscillations is given by dividing eq'n 1 by 2 as,\n",

-      "r=(0.064)**0.5 # m\n",

-      "omega=v_1*((r**2-x_1**2)**0.5) # radians/second\n",

-      "t=(2*pi)/omega # seconds\n",

-      "v_max=r*omega # m/s\n",

-      "\n",

-      "# let the max acceleration be a which is given as,\n",

-      "a=r*omega**2 # m/s^2\n",

-      "\n",

-      "# Results\n",

-      "\n",

-      "print\"(a) The amplitude of oscillations is \",round(r,3),\"m\"\n",

-      "print\"(b) The time period of oscillations is \",round(t,2),\"seconds\"\n",

-      "print\"(c) The maximum velocity is \",round(v_max,2),\"m/s\"\n",

-      "print\"(d) The maximum acceleration is \",round(a,2),\"m/s^2\"\n",

-      "# NOTE: the value of t is incorrect in the text book\n"

-     ],

-     "language": "python",

-     "metadata": {},

-     "outputs": [

-      {

-       "output_type": "stream",

-       "stream": "stdout",

-       "text": [

-        "(a) The amplitude of oscillations is  0.253 m\n",

-        "(b) The time period of oscillations is  1.22 seconds\n",

-        "(c) The maximum velocity is  1.31 m/s\n",

-        "(d) The maximum acceleration is  6.75 m/s^2\n"

-       ]

-      }

-     ],

-     "prompt_number": 14

-    },

-    {

-     "cell_type": "heading",

-     "level": 2,

-     "metadata": {},

-     "source": [

-      "Exammple 24.24-5,Page No:"

-     ]

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [

-      "import math\n",

-      "\n",

-      "# Initilization of variabes\n",

-      "\n",

-      "W=50 # N # weight\n",

-      "x_0=0.075 # m # amplitude\n",

-      "f=1 # oscillation/sec # frequency\n",

-      "pi=3.14\n",

-      "g=9.81 \n",

-      "\n",

-      "# Calculations\n",

-      "\n",

-      "omega=2*pi*f\n",

-      "K=(((2*pi)**2*W)/g)*(10**-2) # N/cm\n",

-      "\n",

-      "# let the total extension of the string be delta which is given as,\n",

-      "delta=(W/K)+(x_0*10**2) # cm\n",

-      "T=K*delta # N # Max Tension\n",

-      "v=omega*x_0 #m/s # max velocity\n",

-      "\n",

-      "# Results\n",

-      "\n",

-      "print\"(a) The stiffness of the spring is \",round(K,2),\"N/cm\"\n",

-      "print\"(b) The maximum Tension in the spring is \",round(T,2),\"N\"\n",

-      "print\"(c) The maximum velocity is \",round(v,2),\"m/s\"\n"

-     ],

-     "language": "python",

-     "metadata": {},

-     "outputs": [

-      {

-       "output_type": "stream",

-       "stream": "stdout",

-       "text": [

-        "(a) The stiffness of the spring is  2.01 N/cm\n",

-        "(b) The maximum Tension in the spring is  65.08 N\n",

-        "(c) The maximum velocity is  0.47 m/s\n"

-       ]

-      }

-     ],

-     "prompt_number": 15

-    },

-    {

-     "cell_type": "heading",

-     "level": 2,

-     "metadata": {},

-     "source": [

-      "Example 24.24-10,Page No:"

-     ]

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [

-      "import math\n",

-      "\n",

-      "# Initilization of variables\n",

-      "\n",

-      "l=1 # m # length of the simple pendulum\n",

-      "g=9.81 # m/s^2\n",

-      "pi=3.14\n",

-      "\n",

-      "# Calculations\n",

-      "\n",

-      "# Let t_s be the time period when the elevator is stationary\n",

-      "t_s=2*pi*(l/g)**0.5 #/ seconds\n",

-      "\n",

-      "# Let t_u be the time period when the elevator moves upwards. Then from eqn 1\n",

-      "t_u=2*pi*((l)/(g+(g/10)))**0.5 # seconds\n",

-      "\n",

-      "# Let t_d be the time period when the elevator moves downwards.\n",

-      "t_d=2*pi*(l/(g-(g/10)))**0.5 # seconds\n",

-      "\n",

-      "# Results\n",

-      "\n",

-      "print\"The time period of oscillation of the pendulum for upward acc of the elevator is \",round(t_u,2),\"seconds\"\n",

-      "print\"The time period of oscillation of the pendulum for downward acc of the elevator is \",round(t_d,2),\"seconds\"\n"

-     ],

-     "language": "python",

-     "metadata": {},

-     "outputs": [

-      {

-       "output_type": "stream",

-       "stream": "stdout",

-       "text": [

-        "The time period of oscillation of the pendulum for upward acc of the elevator is  1.91 seconds\n",

-        "The time period of oscillation of the pendulum for downward acc of the elevator is  2.11 seconds\n"

-       ]

-      }

-     ],

-     "prompt_number": 17

-    },

-    {

-     "cell_type": "heading",

-     "level": 2,

-     "metadata": {},

-     "source": [

-      "Example 24.24-11,Page No:"

-     ]

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [

-      "import math\n",

-      "\n",

-      "# Initilization of variables\n",

-      "\n",

-      "t=1 # second # time period of the simple pendulum\n",

-      "g=9.81 # m/s^2\n",

-      "pi=3.14\n",

-      "\n",

-      "# Calculations\n",

-      "\n",

-      "# Length of pendulum is given as,\n",

-      "l=(t/(2*pi)**2)*g # m\n",

-      "\n",

-      "# Let t_u be the time period when the elevator moves upwards. Then the time period is given as,\n",

-      "t_u=2*pi*((l)/(g+(g/10)))**0.5 # seconds\n",

-      "\n",

-      "# Let t_d be the time period when the elevator moves downwards.\n",

-      "t_d=2*pi*(l/(g-(g/10)))**0.5 # seconds\n",

-      "\n",

-      "# Results\n",

-      "\n",

-      "print\"The time period of oscillation of the pendulum for upward acc of the elevator is \",round(t_u,2),\"seconds\"\n",

-      "print\"The time period of oscillation of the pendulum for downward acc of the elevator is \",round(t_d,2),\"seconds\"\n"

-     ],

-     "language": "python",

-     "metadata": {},

-     "outputs": [

-      {

-       "output_type": "stream",

-       "stream": "stdout",

-       "text": [

-        "The time period of oscillation of the pendulum for upward acc of the elevator is  0.95 seconds\n",

-        "The time period of oscillation of the pendulum for downward acc of the elevator is  1.05 seconds\n"

-       ]

-      }

-     ],

-     "prompt_number": 19

-    },

-    {

-     "cell_type": "heading",

-     "level": 2,

-     "metadata": {},

-     "source": [

-      "Example 24.24-12,Page No:"

-     ]

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [

-      "import math\n",

-      "\n",

-      "# Initilization of variables\n",

-      "\n",

-      "m=15 # kg # mass of the disc\n",

-      "D=0.3 # m # diameter of the disc\n",

-      "R=0.15 # m # radius\n",

-      "l=1 # m # length of the shaft\n",

-      "d=0.01 # m # diameter of the shaft\n",

-      "G=30*10**9 # N-m^2 # modulus of rigidity\n",

-      "pi=3.14\n",

-      "\n",

-      "# Calculations\n",

-      "\n",

-      "# M.I of the disc about the axis of rotation is given as,\n",

-      "I=(m*R**2)*0.5 # kg-m^2\n",

-      "\n",

-      "# Stiffness of the shaft\n",

-      "k_t=(pi*d**4*G)/(32*l) # N-m/radian\n",

-      "t=2*pi*(I/k_t)**0.5 # seconds\n",

-      "\n",

-      "# Results\n",

-      "\n",

-      "print\"The time period of oscillations of the disc is \",round(t,2),\"seconds\"\n"

-     ],

-     "language": "python",

-     "metadata": {},

-     "outputs": [

-      {

-       "output_type": "stream",

-       "stream": "stdout",

-       "text": [

-        "The time period of oscillations of the disc is  0.48 seconds\n"

-       ]

-      }

-     ],

-     "prompt_number": 24

-    },

-    {

-     "cell_type": "code",

-     "collapsed": false,

-     "input": [],

-     "language": "python",

-     "metadata": {},

-     "outputs": [],

-     "prompt_number": 24

-    }

-   ],

-   "metadata": {}

-  }

- ]

-}
\ No newline at end of file