\(\left(\because \cos 2 \theta=1-2 \sin ^{2} \theta\right) \)

\(= \frac{a}{2}-\frac{a \cos 2 \omega t}{2}\)

\(\therefore \quad\) Velocity, \(v=\frac{d x}{d t}=\frac{2 \omega a \sin 2 \omega t}{2}=\omega a \sin 2 \omega t\)

Acceleration, \(a=\frac{d v}{d t}=2 \omega^{2} a \cos 2 \omega t\)

For the given displacement \(x=a \sin ^{2} \omega t,\)

\(a \propto-x\) is not satisfied.

Hence, the motion of the particle is non simple harmonic motion.