The function ${\sin }^2(\omega t)$ represents:

The function $y={\sin }^2(\omega t)$ can be rewritten using a trigonometric identity:
$$y=\frac{1-\cos (2\omega t)}{2}$$
$$y=\frac{1}{2}-\frac{1}{2}\cos (2\omega t)$$
This represents a periodic motion because it is a sum of a constant and a cosine term.It represents Simple Harmonic Motion (SHM) because its acceleration is proportional to the displacement from the mean position $y=1/2$. Specifically, any function of the form $A\cos ({\omega }^{\prime }t+\varphi )$ is SHM.The angular frequency of the SHM is ${\omega }^{\prime }=2\omega$.Time period $T=\frac{2\pi }{{\omega }^{\prime }}=\frac{2\pi }{2\omega }=\frac{\pi }{\omega }$.