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A Basic_Electronics_by_Rakesh_Kumar_Garg,_Ashish_Dixit_&_Paban_Yadav/chapter1.ipynb A Basic_Electronics_by_Rakesh_Kumar_Garg,_Ashish_Dixit_&_Paban_Yadav/chapter2.ipynb A Basic_Electronics_by_Rakesh_Kumar_Garg,_Ashish_Dixit_&_Paban_Yadav/chapter3.ipynb A Basic_Electronics_by_Rakesh_Kumar_Garg,_Ashish_Dixit_&_Paban_Yadav/chapter4.ipynb A Basic_Electronics_by_Rakesh_Kumar_Garg,_Ashish_Dixit_&_Paban_Yadav/chapter5.ipynb A Basic_Electronics_by_Rakesh_Kumar_Garg,_Ashish_Dixit_&_Paban_Yadav/chapter6.ipynb A Basic_Electronics_by_Rakesh_Kumar_Garg,_Ashish_Dixit_&_Paban_Yadav/chapter7.ipynb A Basic_Electronics_by_Rakesh_Kumar_Garg,_Ashish_Dixit_&_Paban_Yadav/chapter8.ipynb A Basic_Electronics_by_Rakesh_Kumar_Garg,_Ashish_Dixit_&_Paban_Yadav/screenshots/DCLOADLINEchapter4.png A Basic_Electronics_by_Rakesh_Kumar_Garg,_Ashish_Dixit_&_Paban_Yadav/screenshots/DCLOADLineCH4.png A Basic_Electronics_by_Rakesh_Kumar_Garg,_Ashish_Dixit_&_Paban_Yadav/screenshots/TransferCharofnchmosfetCH8.png A Engineering_Mechanics_by_A._K._Tayal/Chapter10.ipynb A Engineering_Mechanics_by_A._K._Tayal/Chapter12.ipynb A Engineering_Mechanics_by_A._K._Tayal/Chapter13.ipynb A Engineering_Mechanics_by_A._K._Tayal/Chapter14.ipynb A Engineering_Mechanics_by_A._K._Tayal/Chapter15.ipynb A Engineering_Mechanics_by_A._K._Tayal/Chapter16.ipynb A Engineering_Mechanics_by_A._K._Tayal/Chapter17.ipynb A Engineering_Mechanics_by_A._K._Tayal/Chapter18.ipynb A Engineering_Mechanics_by_A._K._Tayal/Chapter19.ipynb A Engineering_Mechanics_by_A._K._Tayal/Chapter2.ipynb A Engineering_Mechanics_by_A._K._Tayal/Chapter20.ipynb A Engineering_Mechanics_by_A._K._Tayal/Chapter21.ipynb A Engineering_Mechanics_by_A._K._Tayal/Chapter22.ipynb A Engineering_Mechanics_by_A._K._Tayal/Chapter23.ipynb A Engineering_Mechanics_by_A._K._Tayal/Chapter24.ipynb A Engineering_Mechanics_by_A._K._Tayal/Chapter25.ipynb A Engineering_Mechanics_by_A._K._Tayal/Chapter26.ipynb A Engineering_Mechanics_by_A._K._Tayal/Chapter3.ipynb A Engineering_Mechanics_by_A._K._Tayal/Chapter4.ipynb A Engineering_Mechanics_by_A._K._Tayal/Chapter5.ipynb A Engineering_Mechanics_by_A._K._Tayal/Chapter6.ipynb A Engineering_Mechanics_by_A._K._Tayal/Chapter7.ipynb A Engineering_Mechanics_by_A._K._Tayal/Chapter8.ipynb A Engineering_Mechanics_by_A._K._Tayal/Chapter9.ipynb A Engineering_Mechanics_by_A._K._Tayal/screenshots/1.png A Engineering_Mechanics_by_A._K._Tayal/screenshots/2.png A Engineering_Mechanics_by_A._K._Tayal/screenshots/3.png A Semiconductor_circuit_approximations_by_A.P._Malvino/ch10.ipynb A Semiconductor_circuit_approximations_by_A.P._Malvino/ch11.ipynb A Semiconductor_circuit_approximations_by_A.P._Malvino/ch12.ipynb A Semiconductor_circuit_approximations_by_A.P._Malvino/ch14.ipynb A Semiconductor_circuit_approximations_by_A.P._Malvino/ch16.ipynb A Semiconductor_circuit_approximations_by_A.P._Malvino/ch2.ipynb A Semiconductor_circuit_approximations_by_A.P._Malvino/ch3.ipynb A Semiconductor_circuit_approximations_by_A.P._Malvino/ch4.ipynb A Semiconductor_circuit_approximations_by_A.P._Malvino/ch5.ipynb A Semiconductor_circuit_approximations_by_A.P._Malvino/ch6.ipynb A Semiconductor_circuit_approximations_by_A.P._Malvino/ch7.ipynb A Semiconductor_circuit_approximations_by_A.P._Malvino/ch8.ipynb A Semiconductor_circuit_approximations_by_A.P._Malvino/ch9.ipynb A Semiconductor_circuit_approximations_by_A.P._Malvino/screenshots/ACloadLineChapter10.png A Semiconductor_circuit_approximations_by_A.P._Malvino/screenshots/DCandACloadlinechapter9.png A Semiconductor_circuit_approximations_by_A.P._Malvino/screenshots/Powerratingchapter9.png
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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 24 Mechanical Vibrations"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Example 24.1 Simple Harmonic Motion"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "(a) The amplitude of oscillation is 10 cm\n",
+ "(b) The maximum acceleration is 10.966227 cm/s**2\n",
+ "(c) The velocity of the particle at 5 cm from mean position is 9.068997 cm/s\n"
+ ]
+ }
+ ],
+ "source": [
+ "import math\n",
+ "# Initilization of variables\n",
+ "f=1/6 # oscillations/second\n",
+ "x=8 # cm # distance from the mean position\n",
+ "# Calculations\n",
+ "omega=2*math.pi*f\n",
+ "# Amplitude is given by eq'n \n",
+ "r=math.sqrt((25*x**2)/16) # cm\n",
+ "# Maximum acceleration is given as,\n",
+ "a_max=(math.pi/3)**2*10 # cm/s^2\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*math.sqrt(r**2-s**2) # cm/s\n",
+ "# Results\n",
+ "print('(a) The amplitude of oscillation is %d cm'%r)\n",
+ "print('(b) The maximum acceleration is %f cm/s**2'%a_max)\n",
+ "print('(c) The velocity of the particle at 5 cm from mean position is %f cm/s'%v)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Example 24.2 Simple Harmonic Motion"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "(a) The amplitude of oscillations is 0.252982 m\n",
+ "(b) The time period of oscillations is 1.216734 seconds\n",
+ "(c) The maximum velocity is 1.306395 m/s\n",
+ "(d) The maximum acceleration is 6.746192 m/s**2\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Initilization of variables\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",
+ "# assume velocities as v_1 & v_2\n",
+ "v_1=1.2 # m/s\n",
+ "v_2=0.8 # m/s\n",
+ "# Calculations\n",
+ "# The amplitude of oscillations is given by dividing eq'n 1 by 2 as,\n",
+ "r=math.sqrt(0.32/5) # m\n",
+ "omega=v_1/(math.sqrt(r**2-x_1**2)) # radians/second\n",
+ "t=(2*math.pi)/omega # seconds\n",
+ "v_max=r*omega # m/s\n",
+ "# let the max acceleration be a which is given as,\n",
+ "a=r*omega**2 # m/s**2 \n",
+ "# Results\n",
+ "print('(a) The amplitude of oscillations is %f m'%r)\n",
+ "print('(b) The time period of oscillations is %f seconds'%t)\n",
+ "print('(c) The maximum velocity is %f m/s'%v_max)\n",
+ "print('(d) The maximum acceleration is %f m/s**2'%a) # the value of max acc is incorrect in the textbook\n",
+ "# NOTE: the value of t is incorrect in the text book\n",
+ "# The values may differ slightly due to decimal point accuracy"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Example 24.5 Equivalent spring constant"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "(a) The stiffness of the spring is 2.012152 N/cm\n",
+ "(b) The maximum Tension in the spring is 65.091138 N\n",
+ "(c) The maximum velocity is 0.471239 m/s\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Initilization of variabes\n",
+ "W=50 # N # weight\n",
+ "x_0=0.075 # m # amplitude\n",
+ "f=1 # oscillation/sec # frequency\n",
+ "g=9.81 \n",
+ "# Calculations\n",
+ "omega=2*math.pi*f\n",
+ "K=(((2*math.pi)**2*W)/g)*(10**-2) # N/cm\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",
+ "# Results\n",
+ "print('(a) The stiffness of the spring is %f N/cm'%K)\n",
+ "print('(b) The maximum Tension in the spring is %f N'%T)\n",
+ "print('(c) The maximum velocity is %f m/s'%v)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Example 24.10 Pendulum Motion"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The time period of oscillation of the pendulum for upward acc of the elevator is 1.912710 seconds\n",
+ "The time period of oscillation of the pendulum for downward acc of the elevator is 2.114580 seconds\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Initilization of variables\n",
+ "l=1 # m # length of the simple pendulum\n",
+ "g=9.81 # m/s^2\n",
+ "# Calculations\n",
+ "# Let t_s be the time period when the elevator is stationary\n",
+ "t_s=2*math.pi*math.sqrt(l/g) #/ seconds\n",
+ "# Let t_u be the time period when the elevator moves upwards. Then from eqn 1\n",
+ "t_u=2*math.pi*math.sqrt((l)/(g+(g/10))) # seconds\n",
+ "# Let t_d be the time period when the elevator moves downwards.\n",
+ "t_d=2*math.pi*math.sqrt(l/(g-(g/10))) # seconds\n",
+ "# Results\n",
+ "print('The time period of oscillation of the pendulum for upward acc of the elevator is %f seconds'%t_u)\n",
+ "print('The time period of oscillation of the pendulum for downward acc of the elevator is %f seconds'%t_d)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Example 24.11 Pendulum Motion"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The time period of oscillation of the pendulum for upward acc of the elevator is 0.953463 seconds\n",
+ "The time period of oscillation of the pendulum for downward acc of the elevator is 1.054093 seconds\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Initilization of variables\n",
+ "t=1 # second # time period of the simple pendulum\n",
+ "g=9.81 # m/s^2\n",
+ "# Calculations\n",
+ "# Length of pendulum is given as,\n",
+ "l=(t/(2*math.pi)**2)*g # m\n",
+ "# Let t_u be the time period when the elevator moves upwards. Then the time period is given as,\n",
+ "t_u=2*math.pi*math.sqrt((l)/(g+(g/10))) # seconds\n",
+ "# Let t_d be the time period when the elevator moves downwards.\n",
+ "t_d=2*math.pi*math.sqrt(l/(g-(g/10))) # seconds\n",
+ "# Results\n",
+ "print('The time period of oscillation of the pendulum for upward acc of the elevator is %f seconds'%t_u)\n",
+ "print('The time period of oscillation of the pendulum for downward acc of the elevator is %f seconds'%t_d)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Example 24.12 Pendulum Motion"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The time period of oscillations of the disc is 0.475599 seconds\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Initilization of variables\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",
+ "# Calculations\n",
+ "# M.I of the disc about the axis of rotation is given as,\n",
+ "I=(m*R**2)/2 # kg-m**2\n",
+ "# Stiffness of the shaft\n",
+ "k_t=(math.pi*d**4*G)/(32*l) # N-m/radian\n",
+ "t=2*math.pi*math.sqrt(I/k_t) # seconds\n",
+ "# Results\n",
+ "print('The time period of oscillations of the disc is %f seconds'%t)"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.5.1"
+ },
+ "widgets": {
+ "state": {},
+ "version": "1.1.2"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}