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| author | Thomas Stephen Lee | 2015-08-28 16:53:23 +0530 |
|---|---|---|
| committer | Thomas Stephen Lee | 2015-08-28 16:53:23 +0530 |
| commit | db0855dbeb41ecb8a51dde8587d43e5d7e83620f (patch) | |
| tree | b95975d958cba9af36cb1680e3f77205354f6512 /Engineering_Mechanics_by_Tayal_A.K./chapter24_3.ipynb | |
| parent | 5a86a20b9de487553d4ef88719fb0fd76a5dd6a7 (diff) | |
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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": {}
+ }
+ ]
+}
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