From b8bb8bbfa81499ad7fc3f3508be257da65f543af Mon Sep 17 00:00:00 2001 From: nice Date: Tue, 16 Sep 2014 17:48:17 +0530 Subject: updating repo --- Engineering_Physics_Malik/Chapter_7.ipynb | 569 ++++++++++++++++++++++++++++++ 1 file changed, 569 insertions(+) create mode 100644 Engineering_Physics_Malik/Chapter_7.ipynb (limited to 'Engineering_Physics_Malik/Chapter_7.ipynb') diff --git a/Engineering_Physics_Malik/Chapter_7.ipynb b/Engineering_Physics_Malik/Chapter_7.ipynb new file mode 100644 index 00000000..6762cbc5 --- /dev/null +++ b/Engineering_Physics_Malik/Chapter_7.ipynb @@ -0,0 +1,569 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "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": {} + } + ] +} \ No newline at end of file -- cgit