Question
Wed February 13, 2013 By: Ankush Sharma
 

The initial position and velocity of a body moving in SHM with period T=0.25s are x=5.0 cm and v=218cm/s. What are the amplitude and phase constant of the motion?

Expert Reply
Wed May 08, 2013
Lets suppose the equation of motion of the particle is
 
x=Asin(wt + p) ....1 ; A- amplitude, p- phase constant, w=2?/T
 
Differentiating the above equation, we get
 
v=Awcos(wt + p)
or, v/w = Acos(wt + p).... 2
 
Square and add eqn 1 and 2, we get
 
x2 + (v/w)2 = A2
 
Now putting these values we get
 
A2 = 25 + (218/8?)2 = 100
 
So A = 10 cm
 
Now putting this value in eqn 1 for t=0, we have x=5
Hence
5=10sin(p) 
or p = 30 degrees is the phase constant.
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