Does the function `y=cos^(2)omegat ` represent a periodic of a simple harmonic motion? What is the period of the motion?

Does the function y = sin^2 omegat represent a periodic or a simple harmonic motion ? What is the period of the motion ?

Difference between periodic motion and simple harmonic motion.

Show that the equation x=acos^(2)omegat represents a simple harmonic motion. Find the (i) amplitude, (ii) time period and (iii) position of equilibrium of the particle.

The funtion of time representing a simple harmonic motion with a period of pi/omega is :