Chapter 13:Vibrations and Waves

Ex13.1:pg-508

  import math   #Example  13_1
  
  #To find the maximum velocity and acceleration and the same when x=10cm
xo=0.4       #Units in Meters
k=24.5         #Units in N/M
m=2             #Units in Kg
vmax=xo*(math.sqrt(k/m))         #Units in meters/sec
print "Maximum velocity is Vmax=",round(vmax,1)," Meter/sec\n"
amax=(k*xo)/m              #Units in meter/sec**2
print "Maximum acceleration is Amax=",round(amax,1)," meter/sec**2\n"
x=0.1            #Units in meters
v=math.sqrt((k/m)*(xo**2-x**2))          #Units in meters/Sec
print "Velocity at x=0.1 meters is= ",round(v,2)," meters/sec\n"
a=-(k*x)/m   #Units in meter/sec**2
print "Acceleration at x=0.1 meters is= ",round(a,2)," meters/sec**2\n"

Maximum velocity is Vmax= 1.4  Meter/sec

Maximum acceleration is Amax= 4.9  meter/sec**2

Velocity at x=0.1 meters is=  1.36  meters/sec

Acceleration at x=0.1 meters is=  -1.23  meters/sec**2

Ex13.2:pg-512

  import math   #Example  13_2
 
 
  #To find the frequency of the vibrations
spring=24.5         #Units in N/m
m=2        #Units in Kg
f=(1/(2*math.pi))*math.sqrt(spring/m)          #Units in Hz
print "The frequency of vibrations is f=",round(f,2)," Hz"

The frequency of vibrations is f= 0.56  Hz

Ex13.3:pg-513

  import math   #Example  13_3
 
  
  #To find the tension required in string
m=0.002           #Units in Kg
l=0.6          #Units in meters
v=300       #Units in meters/sec
T=(m/l)*v**2       #Units in N
print "Tension required in the string is T=",round(T)," N"

Tension required in the string is T= 300.0  N

Ex13.4:pg-514

  import math   #Example  13_4
 
  
  #To draw a picture on the first three resonance frequencies
l=6        #Units in meters
n=1
lamda1=(2*l)/n        #Units in meters
n=2
lamda2=(2*l)/n        #Units in meters
n=3
lamda3=(2*l)/n        #Units in meters
speed=24         #Units in meters/sec
f1=speed/lamda1             #Units in Hz
f2=speed/lamda2             #Units in Hz
f3=speed/lamda3             #Units in Hz
print "The first resonance frequency is F1=",round(f1)," Hz\n"
print "The second resonance frequency is F2=",round(f2)," Hz\n"
print "The third resonance frequency is F3=",round(f3)," Hz\n"

The first resonance frequency is F1= 2.0  Hz

The second resonance frequency is F2= 4.0  Hz

The third resonance frequency is F3= 6.0  Hz

Ex13.5:pg-515

  import math   #Example  13_5
 
  
  #To find the speed of the wave
l=300*10**-2       #Units in Meters
lamda3=(l*2)/3       #Units in meters
f=20         #Units in sec**-1 or Hz
v=f*lamda3         #Units in meters/sec
print "The speed of the wave is v=",round(v)," meters/sec"

The speed of the wave is v= 40.0  meters/sec

Ex13.6:pg-516

  import math   #Example  13_6
 
  
  #To find the youngs modulus
lamda=1.85      #Units in meters
f=2700       #units in sec**-1
v=lamda*f        #Units in meters/sec
density=7.86*10**3        #Units in Kg/meter**3
y=v**2*density     #Units in N/meters**2
print "The youngs modulus is Y="
print round(y,-8),"N/meters**2"

The youngs modulus is Y=
1.961e+11 N/meters**2