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Question

How long after the beginning of motion is the displacement of a harmonically oscillating point equal to one half its amplitude,if the period is 24 sec and initial phase is zero?


Solution

time peroid: 24 s
thus frequency: 1/T = 1/24 Hz = w
 
if we take the amplitude to be A

and the equation of motion to be:
x = A sin(wt)
 
thus at x = A/2   A/2 = A sin( (2π/T)t)
 
1/2=sin(( 2 π /24) t )
 
We know,sin(π/6)=1/2

π/6=(2π/24)t

1/6=1/12 t

t=12/6

t = 2 sec
 

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