The displacement of a particle along the X-axis is given by x=a sin2ωt.. The motion of the particle corresponds to

For a SHM,  acceleration, a=d2xdt2=-ω2x                          …(i)According to the question,                               x=a sin2ωt=a1-cos2ωt2Differentiating the above expression w.r.t. t, we get                 dxdt=aω sin 2ωtAgain, differentiating x w.r.t. t, we get            d2xdt2=2aω2 cos 2ωtor        d2xdt2=2aω21-2sin2ωt⇒  d2xdt2=2aω2-4aω2sin2ωt=2aω2-4ω2x              …(ii)Therefore, after comparing Eqs. (i) and (ii), we can say that the motion of the particle is non-simple harmonic motion.