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{
"metadata": {
"name": "",
"signature": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 3, Forced harmonic oscillator & resonance"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1, page 135"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from __future__ import division\n",
"from math import sqrt, degrees, atan, pi\n",
"# Phase shift\n",
"#given data :\n",
"F0=25 # in N\n",
"m=1 \n",
"f0=F0/m \n",
"K=1*10**3 # in N/m\n",
"w0=sqrt(K/m) \n",
"b=0.05 # in N-s/m\n",
"r=b/(2*m) # in s**-1\n",
"A=f0*10**3/sqrt(9*w0**4+(16*r**2*(w0)**2)) \n",
"print \"The amplitude, A = %0.2f mm \" %A\n",
"p=2*w0 \n",
"fi=atan(2*r*p/(w0**2-p**2)) # radian \n",
"fi = degrees(fi) # degree\n",
"print \"Phase shift is\",round(fi,2),\"degree or\",round(fi*(pi/180),3),\"radian.\"\n",
"#phase shift is converted wrong into radians"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The amplitude, A = 8.33 mm \n",
"Phase shift is -0.06 degree or -0.001 radian.\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2, page 136"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from numpy import array\n",
"# A/Amax\n",
"x1=array([0.99,0.98,0.97]) #\n",
"wt=50 #\n",
"wo=1 #assume\n",
"fo=1 #assume\n",
"for x in x1:\n",
" a=((fo/((wo**2)*((1-x**2)**2+((1/wt**2)*x**2))**(1/2)))) #\n",
" am=fo/((wo**2)*(1/wt**2)**(1/2)) #\n",
" z=a/am #\n",
" print \"For p/wo\",x,\", value of A/Amax is\",round(z,2)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"For p/wo 0.99 , value of A/Amax is 0.71\n",
"For p/wo 0.98 , value of A/Amax is 0.45\n",
"For p/wo 0.97 , value of A/Amax is 0.32\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 3, page 154"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import pi, sqrt\n",
"# Reactance and impedence\n",
"#given data :\n",
"n=50 # in cycles\n",
"w=2*pi*n # in rad/sec\n",
"L=1/pi # in H\n",
"XL=w*L \n",
"print \"The reactance, XL = %0.0f ohm \" %XL\n",
"R=100 # in ohm\n",
"Z=sqrt(R**2+XL**2) \n",
"print \"The impedence, Z = %0.1f ohm \" %Z"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The reactance, XL = 100 ohm \n",
"The impedence, Z = 141.4 ohm \n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4, page 155"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import sqrt, pi\n",
"# Current and Capacity\n",
"#given data :\n",
"E=110 # in V\n",
"R=10 # in ohm\n",
"L=1*10**-3 # in H\n",
"C=1*10**-6 # in F\n",
"n=10000 # in Hz\n",
"w=2*pi*n \n",
"I=E/sqrt(R**2+((w*L)-(1/(w*C)))**2) \n",
"print \"The current, I = %0.2f A \" %I\n",
"L1=1/(w**2*C) \n",
"print \"The value of capacity, L1 = %0.2e F \" %L1\n",
"#Capacitance is calculated wrong in the textbook"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The current, I = 2.29 A \n",
"The value of capacity, L1 = 2.53e-04 F \n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 5, page 155"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from math import sqrt\n",
"# Resonent frequency and Separation\n",
"#given data :\n",
"L=1*10**-3 # in H\n",
"C=0.1*10**-6 # in F\n",
"w0=1/sqrt(L*C) \n",
"print \"Resonant frequency, w0 = %0.e rad/s \" %w0\n",
"R=10 # in ohm\n",
"w2_w1=R/L \n",
"print \"The separation = %0.e rad/s \" %w2_w1\n",
"S=w0/w2_w1 \n",
"print \"The sharpness = %0.f \" %S"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Resonant frequency, w0 = 1e+05 rad/s \n",
"The separation = 1e+04 rad/s \n",
"The sharpness = 10 \n"
]
}
],
"prompt_number": 16
}
],
"metadata": {}
}
]
}
|
