Hello,

The position of particle in X direction varies as :

x = A sin(wt )............ ( 1 )

Differentiate the above equation with respect to time to find the velocity of particle at any instant:

So, dx / dt = v = w.A.cos(wt)......... ( 2 )

Now, we know that acceleration is the rate of change of velocity with respect to time.

So, now differentiating equation 2 with respect to time to find velocity.

a = dv / dt = -w^2. A. ( sin wt )

From eqn 1,

a = - w^2 . x

So, the acceleration of particle varies as, a = - w^2 . x

Best Wishes.