From db0855dbeb41ecb8a51dde8587d43e5d7e83620f Mon Sep 17 00:00:00 2001 From: Thomas Stephen Lee Date: Fri, 28 Aug 2015 16:53:23 +0530 Subject: add books --- .../chapter24_3.ipynb | 349 +++++++++++++++++++++ 1 file changed, 349 insertions(+) create mode 100755 Engineering_Mechanics_by_Tayal_A.K./chapter24_3.ipynb (limited to 'Engineering_Mechanics_by_Tayal_A.K./chapter24_3.ipynb') diff --git a/Engineering_Mechanics_by_Tayal_A.K./chapter24_3.ipynb b/Engineering_Mechanics_by_Tayal_A.K./chapter24_3.ipynb new file mode 100755 index 00000000..9fcc267a --- /dev/null +++ b/Engineering_Mechanics_by_Tayal_A.K./chapter24_3.ipynb @@ -0,0 +1,349 @@ +{ + "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 -- cgit