path: root/Engineering_Physics_by_H_K_Malik/7-WAVES_AND_OSCILLATIONS.ipynb

{
"cells": [
 {
		   "cell_type": "markdown",
	   "metadata": {},
	   "source": [
       "# Chapter 7: WAVES AND OSCILLATIONS"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 7.10: Calculation_of_Time_period_of_pendulum.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
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	   "outputs": [],
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"clc \n",
"// Given that\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",
"// Sample Problem 10 on page no. 7.25\n",
"printf('\n # PROBLEM 10 # \n')\n",
"T = 2 * %pi * sqrt(l / (g + f))\n",
"printf('\n Standard formula used \n T = 2 * pi * sqrt(l / (g + f)). \n ') \n",
"printf('\n Time period of pendulum = %f sec.',T)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 7.11: Calculation_of_Time_period_of_motion.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
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	   "outputs": [],
"source": [
"clc \n",
"// Given that\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",
"// Sample Problem 11 on page no. 7.26\n",
"printf('\n # PROBLEM 11 # \n')\n",
"k = (m1 * g) / x\n",
"T = (2 * %pi) * sqrt(m2 / k)\n",
"printf('\n Standard formula used \n k = (m1 * g) / x. \n T = (2 * pi) * sqrt(m2 / k).\n')\n",
"printf('\n Time period of motion = %f sec. ',T)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 7.12: EX7_12.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
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	   "outputs": [],
"source": [
"clc \n",
"// Given that\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",
"// Sample Problem 12 on page no. 7.26\n",
"printf('\n # PROBLEM 12 # \n')\n",
"k = F / x\n",
"F_ = m * g\n",
"x_ = F_ / k\n",
"T = (2 * %pi) * sqrt(m / k)\n",
"printf('\n Standard formula used \n k = F / x. \n F_ = m * g. \n x_ = F_ / k. \n T = (2 * pi) * sqrt(m / k). \n ')\n",
"printf('\n Time period of motion = %f sec. \n Compression of the spring due to the weight of the body = %f m. ',T,x_)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 7.13: Calculation_of_Time.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc \n",
"// Given that\n",
"t = 50 // relaxation time in sec\n",
"r = 1 / exp(1) // falls in amplitude and energy\n",
"// Sample Problem 13 on page no. 7.26\n",
"printf('\n # PROBLEM 13 # \n')\n",
"s = 1 / (2 * t)\n",
"T = 1 / s // by using formula A=A_exp(-st) and using r=A/A_\n",
"printf('\n Standard formula used \n s = 1 / (2 * t). \n T = 1 / s . \n ')\n",
"printf('\n Time = %f sec',T)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 7.14: Calculation_of_Time.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc \n",
"// Given that\n",
"n = 260 // frequency in Hz\n",
"Q = 2000 // quality factor\n",
"r = 1 / (exp(1)^2) // decrease in amplitude \n",
"// Sample Problem 14 on page no. 7.27\n",
"printf('\n # PROBLEM 14 # \n')\n",
"tou = Q / (2 * %pi * n)\n",
"t = 2 * tou // by using formula A=A_exp(-st) and using r=A/A_\n",
"printf('\n Standard formula used \n tou = Q / (2 * pi * n). \n t = 2 * tou. \n')\n",
"printf('\n Time = %f sec.',t)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 7.1: Calculation_of_Amplitude_and_Mass_of_particle.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc \n",
"// Given that\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",
"// Sample Problem 1 on page no. 7.22\n",
"printf('\n # PROBLEM 1 # \n')\n",
"A = x / sin((2 * %pi * t) / T)\n",
"M = (E * T^2) / (2 * %pi^2 * A^2)\n",
"printf('\n Standard formula used \n A = x / sin((2 * pi * t) / T). \n M = (E * T^2) / (2 * pi^2 * A^2). \n')\n",
"printf('\n Amplitude = %f meter,\n Mass of particle = %f g',A,M/1e-3)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 7.2: Calculation_of_Maximum_amplitude_of_velocity.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc \n",
"// Given that\n",
"A = 0.05 // amplitude in meter\n",
"T = 10 // time period of S.H.M. in sec\n",
"// Sample Problem 2 on page no. 7.22\n",
"printf('\n # PROBLEM 2 # \n')\n",
"v = (A * 2 * %pi) / T\n",
"printf('\n Standard formula used \n v = (A * 2 * pi) / T')\n",
"printf('\n Maximum amplitude of velocity = %f meter/sec',v)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 7.3: 3Calculation_of_Force_constant_and_Time_period.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc \n",
"// Given that\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",
"// Sample Problem 3 on page no. 7.23\n",
"printf('\n # PROBLEM 3 # \n')\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",
"printf('Standard formula used \n k.E.=1/2*k*A^2,\n T=2*pi*sqrt(m/k)\n')\n",
"printf('\n Force constant = %f J/m,\n Time period = %f sec',k,T)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 7.4: Calculation_of_Time_taken_by_the_particle.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc \n",
"// Given that\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",
"// Sample Problem 4 on page no. 7.23\n",
"printf('\n # PROBLEM 4 # \n')\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",
"printf('\n Standard formula used \n x=Asin(wt+delta). \n ')\n",
"printf('\n Time taken by the particle = %f sec',t)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 7.5: Calculation_of_Maximum_velocity_and_acceleration.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc \n",
"// Given that\n",
"A = 0.05// amplitude in meter\n",
"T = 10 * %pi // time period of s.h.m. in sec\n",
"// Sample Problem 5 on page no. 7.24\n",
"printf('\n # PROBLEM 5 # \n')\n",
"v = A * (2 * %pi / T)\n",
"a = A * (2 * %pi / T)^2\n",
"printf('\n Standard formula used \n v = A * (2 * pi / T). \n a = A * (2 * pi / T)^2. \n ')\n",
"printf('\n Maximum velocity = %e meter/sec,\n acceleration = %e m/sec^2',v,a)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 7.6: Calculation_of_Maximum_velocity.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc \n",
"// Given that\n",
"A = 0.06// amplitude in meter\n",
"T = 10 * %pi // time period of s.h.m. in sec\n",
"// Sample Problem 6 on page no. 7.24\n",
"printf('\n # PROBLEM 6 # \n')\n",
"v = A * (2 * %pi / T)\n",
"printf('\n Standard formula used \n v = A * (2 * pi / T)')\n",
"printf('\n Maximum velocity = %e meter/sec',v)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 7.7: Calculation_of_natural_frequency.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc \n",
"// Given that\n",
"k = 16 // stiffness constant of spring n/m\n",
"m = 1 // mass of particle in kg\n",
"// Sample Problem 7 on page no. 7.24\n",
"printf('\n # PROBLEM 7 # \n')\n",
"n = sqrt(k / m) / (2 * %pi)\n",
"printf('\n Standard formula used \n n = sqrt(k / m) / (2 * pi).\n')\n",
"printf('\n natural frequency = %f Hz.',n)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 7.8: Calculation_of_The_time_period_of_pendulum.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc \n",
"// Given that\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",
"// Sample Problem 8 on page no. 7.25\n",
"printf('\n # PROBLEM 8 # \n')\n",
"T = 2 * %pi * sqrt(l / g)\n",
"printf('\n Standard formula used \n T = 2 * pi * sqrt(l / g). \n')\n",
"printf('\n The time period of pendulum = %f sec.',T)"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 7.9: Calculation_of_Frequency.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"clc \n",
"// Given that\n",
"m = 100 // mass of particle in gm\n",
"// Sample Problem 9 on page no. 7.25\n",
"printf('\n # PROBLEM 9 # \n')\n",
"n = (1 / (2 * %pi)) * sqrt(10 / m) // by using given formula \n",
"printf('\n Standard formula used \n n = (1 / (2 * pi)) * sqrt(10 / m). \n')\n",
"printf('\n Frequency  = %f Hz.',n)"
   ]
   }
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