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Question

A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is 1a s. The value of a to the nearest integer is.

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Solution

Time period (T)=2 s
Assume particle starts from its mean position (t=0,x=0), so its equation, x=Asin(ωt)

Let particle takes time t1 to move from mean position to half of its amplitude.
A2=Asin(2πT)t

12=sin(2πT)t

π6=2πTt

t=16 s=1a s

a=6

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