From v = vo cos ω t = x0 ω cos ω t

where xo is the maximum displacement

differentiating we get

 a = d v d t =  ω2 ( x 0 s i n ω t ) =  ω2 x
  Variation with time of acceleration   

In terms of x:

Therefore,  a = - xo ω2 sin ω t
                   = - ω2 (xo sin ω t)
which is the defining equation for S.H.M. !
               a     = - ω2 x
Variation with displacement of acceleration  

        a = – a0sin ω t          

where ao is the maximum acceleration
where by a0 = ω2 (xo)