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+{
+"cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 16: Oscillation"
+ ]
+ },
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16.1: Sample_Problem_1.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Given that\n",
+"m = 680*10^-3 //in kg\n",
+"k = 65 //in N/m\n",
+"x = 11*10^-2 //in meter\n",
+"\n",
+"//Sample Problem 16-1a\n",
+"printf('**Sample Problem 16-1a**\n')\n",
+"w = sqrt(k/m)\n",
+"f = 2*%pi/w\n",
+"T = 1/f\n",
+"printf(' Angular Frequency - %f rad/s\n', w)\n",
+"printf(' Frequency\t - %f Hz\n', f)\n",
+"printf(' Time Period\t - %f s\n', T)\n",
+"\n",
+"//Sample Problem 16-1b\n",
+"printf('\n**Sample Problem 16-1b**\n')\n",
+"A = x\n",
+"printf('The amplitude of oscillation is %fcm\n', A*100)\n",
+"\n",
+"//Sample Problem 16-1c\n",
+"printf('\n**Sample Problem 16-1c**\n')\n",
+"Vmax = A*w\n",
+"printf('The maximum speed of the block is %fm/s\n', Vmax)\n",
+"\n",
+"//Sample Problem 16-1d\n",
+"printf('\n**Sample Problem 16-1d**\n')\n",
+"aMAX = Vmax*w\n",
+"printf('The maximum acceleration of the block is %fm/s^2\n', aMAX)\n",
+"\n",
+"//Sample Problem 16-1e\n",
+"printf('\n**Sample Problem 16-1e**\n')\n",
+"//at t=0 x = A\n",
+"phi = acos(x/A)\n",
+"printf('The phase constant for the SHM x=Acos(w*t+phi) is 2*n*pi + %d where n is an integer', phi)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16.2: Sample_Problem_2.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Given that\n",
+"x0 = -8.50*10^-2 //in m\n",
+"v0 = -0.920 //in m/s\n",
+"a0 = 47 //in m/s^2\n",
+"exec('degree_rad.sci', -1)\n",
+"\n",
+"//Sample Problem 16-2a\n",
+"printf('**Sample Problem 16-2a**\n')\n",
+"w = sqrt(-a0/x0)\n",
+"printf('The angular frequency of SHM is equal to %frad/s\n', w)\n",
+"\n",
+"//Sample Problem 16-2b\n",
+"printf('\n**Sample Problem 16-2b**\n')\n",
+"phi = atan(-(v0/x0)/w)\n",
+"A = x0/cos(phi)\n",
+"printf('The value of phi is %f degrees\n', rtod(phi))\n",
+"printf('The maximum value of displacement is equal to %fcm\', A*100)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16.3: Sample_Problem_3.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Sample Problem 16-3a\n",
+"printf('**Sample Problem 16-3a**\n')\n",
+"k = 65 //in N/m\n",
+"A = 11*10^-2 //in meter\n",
+"v = 0 //in m/s\n",
+"E = 0.5*k*A^2 + 0\n",
+"printf('The mechanical energy of the block is %fJ\n', E)\n",
+"\n",
+"//Sample Problem 16-3b\n",
+"printf('\n**Sample Problem 16-3b**\n')\n",
+"x = A/2\n",
+"U = 0.5*k*x^2\n",
+"K = E-U\n",
+"printf('The potential energy at that position is %fJ\n', U)\n",
+"printf('The kinetic energy of the block is %fJ', K)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16.4: Sample_Problem_4.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Given that\n",
+"L = 12.4*10^-2 // in meter\n",
+"m = 135*10^-3 //in kg\n",
+"Ta = 2.53 //in sec\n",
+"Tb = 4.76 //in sec\n",
+"\n",
+"//Sample Problem 16-4\n",
+"printf('**Sample Problem 16-4**\n')\n",
+"//Time period is directly proportional to the squre root of rotational inertial\n",
+"Ia = m*L^2/12\n",
+"I = Ia*(Tb/Ta)^2\n",
+"printf('The rotational inertail of X is %ekg.m^2', I)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16.5: Sample_Problem_5.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Given that\n",
+"L = 1.0 //in meter\n",
+"g = 9.8 //in m/s^2\n",
+"\n",
+"//Sample Problem 16-5a\n",
+"printf('**Sample Problem 16-5a**\n')\n",
+"//(say)\n",
+"m = 1\n",
+"I = (1/3)*m*L^2\n",
+"T = 2*%pi*sqrt(I/(m*g*(L/2)))\n",
+"printf('The time period of SHm is %fs\n', T)\n",
+"\n",
+"//Sample Problem 16-5b\n",
+"printf('\n**Sample Problem 16-5b**\n')\n",
+"Lo = (T/(2*%pi))^2*g\n",
+"printf('The distance of center of oscillation from the pivot is %fcm', Lo*100)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16.6: Sample_Problem_6.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Given that\n",
+"L = 2.0 //in meter\n",
+"m = 12 //in kg\n",
+"k = 1300 //in N/m\n",
+"\n",
+"//Sample Problem 16-6\n",
+"printf('**Sample Problem 16-6**\n')\n",
+"//I*a/L = -k*x*L\n",
+"I = m*L^2/3\n",
+"w = sqrt(k*L*L/I)\n",
+"T = 2*%pi/w\n",
+"printf('The time period of oscillation is %fs', T)"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 16.7: Sample_Problem_7.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Given that\n",
+"m = 250*10^-3 //in kg\n",
+"k = 85 //in N/m\n",
+"b = 70*10^-3 //in kg/s\\n",
+"g = 9.8 //in m/s^2\n",
+"\n",
+"//Sample Problem 16-7a\n",
+"printf('**Sample Problem 16-7a**\n')\n",
+"T = 2*%pi*sqrt(m/k)\n",
+"printf('The time period of oscillation is %fs\n', T)\n",
+"\n",
+"//Sample Problem 16-7b\n",
+"printf('\n**Sample Problem 16-7b**\n')\n",
+"//b*t/(2*m) = log(2)\n",
+"t = log(2)*2*m/b\n",
+"printf('The time taken to drop the amplitude half of its value is %fs\n', t)\n",
+"\n",
+"//Sample Problem 16-7c\n",
+"printf('\nb**Sample Problem 16-7c**\n')\n",
+"//amplitude should drop to A/sqrt(2) from A\n",
+"tE = t/2\n",
+"printf('The time taken to drop the mechanical energy half of its initial value is %fs', tE)"
+ ]
+ }
+],
+"metadata": {
+ "kernelspec": {
+ "display_name": "Scilab",
+ "language": "scilab",
+ "name": "scilab"
+ },
+ "language_info": {
+ "file_extension": ".sce",
+ "help_links": [
+ {
+ "text": "MetaKernel Magics",
+ "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+ }
+ ],
+ "mimetype": "text/x-octave",
+ "name": "scilab",
+ "version": "0.7.1"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
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