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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 13:Vibrations and Waves"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex13.1:pg-508## "
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Maximum velocity is Vmax= 1.4 Meter/sec\n",
"\n",
"Maximum acceleration is Amax= 4.9 meter/sec**2\n",
"\n",
"Velocity at x=0.1 meters is= 1.36 meters/sec\n",
"\n",
"Acceleration at x=0.1 meters is= -1.23 meters/sec**2\n",
"\n"
]
}
],
"source": [
" import math #Example 13_1\n",
" \n",
" #To find the maximum velocity and acceleration and the same when x=10cm\n",
"xo=0.4 #Units in Meters\n",
"k=24.5 #Units in N/M\n",
"m=2 #Units in Kg\n",
"vmax=xo*(math.sqrt(k/m)) #Units in meters/sec\n",
"print \"Maximum velocity is Vmax=\",round(vmax,1),\" Meter/sec\\n\"\n",
"amax=(k*xo)/m #Units in meter/sec**2\n",
"print \"Maximum acceleration is Amax=\",round(amax,1),\" meter/sec**2\\n\"\n",
"x=0.1 #Units in meters\n",
"v=math.sqrt((k/m)*(xo**2-x**2)) #Units in meters/Sec\n",
"print \"Velocity at x=0.1 meters is= \",round(v,2),\" meters/sec\\n\"\n",
"a=-(k*x)/m #Units in meter/sec**2\n",
"print \"Acceleration at x=0.1 meters is= \",round(a,2),\" meters/sec**2\\n\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex13.2:pg-512## "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The frequency of vibrations is f= 0.56 Hz\n"
]
}
],
"source": [
" import math #Example 13_2\n",
" \n",
" \n",
" #To find the frequency of the vibrations\n",
"spring=24.5 #Units in N/m\n",
"m=2 #Units in Kg\n",
"f=(1/(2*math.pi))*math.sqrt(spring/m) #Units in Hz\n",
"print \"The frequency of vibrations is f=\",round(f,2),\" Hz\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex13.3:pg-513"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Tension required in the string is T= 300.0 N\n"
]
}
],
"source": [
" import math #Example 13_3\n",
" \n",
" \n",
" #To find the tension required in string\n",
"m=0.002 #Units in Kg\n",
"l=0.6 #Units in meters\n",
"v=300 #Units in meters/sec\n",
"T=(m/l)*v**2 #Units in N\n",
"print \"Tension required in the string is T=\",round(T),\" N\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex13.4:pg-514"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The first resonance frequency is F1= 2.0 Hz\n",
"\n",
"The second resonance frequency is F2= 4.0 Hz\n",
"\n",
"The third resonance frequency is F3= 6.0 Hz\n",
"\n"
]
}
],
"source": [
" import math #Example 13_4\n",
" \n",
" \n",
" #To draw a picture on the first three resonance frequencies\n",
"l=6 #Units in meters\n",
"n=1\n",
"lamda1=(2*l)/n #Units in meters\n",
"n=2\n",
"lamda2=(2*l)/n #Units in meters\n",
"n=3\n",
"lamda3=(2*l)/n #Units in meters\n",
"speed=24 #Units in meters/sec\n",
"f1=speed/lamda1 #Units in Hz\n",
"f2=speed/lamda2 #Units in Hz\n",
"f3=speed/lamda3 #Units in Hz\n",
"print \"The first resonance frequency is F1=\",round(f1),\" Hz\\n\"\n",
"print \"The second resonance frequency is F2=\",round(f2),\" Hz\\n\"\n",
"print \"The third resonance frequency is F3=\",round(f3),\" Hz\\n\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex13.5:pg-515 "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The speed of the wave is v= 40.0 meters/sec\n"
]
}
],
"source": [
" import math #Example 13_5\n",
" \n",
" \n",
" #To find the speed of the wave\n",
"l=300*10**-2 #Units in Meters\n",
"lamda3=(l*2)/3 #Units in meters\n",
"f=20 #Units in sec**-1 or Hz\n",
"v=f*lamda3 #Units in meters/sec\n",
"print \"The speed of the wave is v=\",round(v),\" meters/sec\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ex13.6:pg-516"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The youngs modulus is Y=\n",
"1.961e+11 N/meters**2\n"
]
}
],
"source": [
" import math #Example 13_6\n",
" \n",
" \n",
" #To find the youngs modulus\n",
"lamda=1.85 #Units in meters\n",
"f=2700 #units in sec**-1\n",
"v=lamda*f #Units in meters/sec\n",
"density=7.86*10**3 #Units in Kg/meter**3\n",
"y=v**2*density #Units in N/meters**2\n",
"print \"The youngs modulus is Y=\"\n",
"print round(y,-8),\"N/meters**2\"\n"
]
}
],
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