Question

The position x of particle moving along x axis varies with time t as x=Asin(wt) where A and w are positive constants. The acceleration a of particle varies with its position (x) as (1)a=Ax (2)a=-w^2x (3)a=Awx (4)a=w^2xA
Pls give brief explanation

Answer 1

V=dx/dt=Asin(wt) /dt = Acos(wt) (w)
Redifferentiate

a=dv/dt =Awcos(wt) /dt=Aw - sin (wt) w

a= - Aw^2sin(wt)