A body is performing simple harmonic motion with amplitude `a` and time period `T` variation of its acceleration `(f)` with time`(t)` is shown in figure If at time `t` velocity of the body is `v` which of the following graph is correct?

Options

A.
B.
C.
D.

Answer

A

Explanation

From graph of acceleration and time graph
`f=f_(max)cosomegat=-(omega^2A)cosomegat`
And we have relationship between acceleration and position as `f=-omega^2ximpliesx=Acosomegat`
which gives `v=(dx)/(dt)=-Aomegasinomegat=-v_(max)sinomegat`
Hence option (a) is correct.