The displacement-time graph of a particle executing simple harmonic motion is shown in the figure

Which one of the following graphs is the correct forcetime graph for the motion of the particle ?

Options

A.
B.
C.
D.

Answer

C

Explanation

The displacement time graph shown in the figure, corresponds to the S.H.M. equation `x=A "sin" omega t`
`therefore v=(dx)/(dt)=A omega "cos" omega t and a= - A omega^(2)"sin" omega t`
`therefore` Force acting on the particle
`= F= ma = - m A omega^(2)"sin" omega t= - m omega^(2) (A "sin" omega t)`
`therefore` The force acting on the particle is a negative "sin"e function. The graph (c ) is the correct force-time graph of the particle.