The equation of motion of a particle is x = a cos (αt)2. The motion is

As the given equation is                 x = a cos (αt)2is a cosine function. Hence, it is an oscillatory motion.Now, putting (t + T) in place of t,     x(t+T)=a cos [α(t+T)]2                                 ∵x(t)=a cos(αt)2                 =a cos αt2+αT2+2αtT≠x(t)where, T is supposed as period of the function ω (t).Hence, it is not periodic.