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Two collinear harmonic oscillations x1 = 8 sin (100 pt) and x2 = 12 sin (96 pt) are superposed. Calculate the (i) maximum and minimum amplitudes, and (ii) the frequency of amplitude modulation.


 Two collinear harmonic oscillations x1 = 8 sin (100 pt) and x2 = 12 sin (96 pt) are


superposed. Calculate the (i) maximum and minimum amplitudes, and (ii) the frequency of


amplitude modulation.


Grade:

1 Answers

Kalash Sharma
15 Points
5 years ago
(a) The amplitude of the resultant oscillation will be
   a = √a1^2 + a2^2 + a1a2 cos(fi1- fi2)   this eauaequa 1}
Given
a1= 8 and a2 = 12
fi1= 100πt and fi2 = 96πt
Put these value in eqyatequ (1)
a=√(8)^2 +(12)^2 +2(8)(12) cos (100πt-96πt)
a=√208+192 cos(4πt)
(1). Maximum, will be
4πt= 2πn
t=n/2 , n= 0,1,2,...,n
(2). Minimum , will be at
4πt=π+-2πn
t= 1/4+-n/2 ,n= 0,1,2,...,n.
 
(2) frequency of amplitude modulation:
f= Umaga modulation/2π = umaga1 - umaga 2/4π  these equation (2)
Given 
Umaga1= 100π and umagU2= 96π
Put these value in equation (2)
f= 100π-96π/4π
f=4π/4π
f=1

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