The oscillation of a body on a smooth horizontal surface is represented by the equation,
`X = A cos (omega t)`
where, X = displacement at time t
`omega =` frequency of oscillation
Which one of the following graphs shows correctly the variation a with t?
Here, a = acceleration at time t
T = time period

Options

A.
B.
C.
D.

Answer

C

Explanation

Here. `X=Acosomegat`
`therefore` Velocity, `v=(dX)/(dt)=(d)/(dt)(Acosomegat)=-Aomegasinomegat`
Acceleration, `a=(dv)/(dt)=(d)/(dt)(-Aomegasinomegat)=-Aomega^(2)cosomegat`
Hence the variation of a with t is correctly shown by graph (c ).