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

Explanation

To determine if the function \( y = \cos^2(\omega t) \) represents a periodic motion of simple harmonic motion (SHM) and to find the period of the motion, we will follow these steps:

### Step 1: Understand the Function
The given function is \( y = \cos^2(\omega t) \). We need to analyze this function to see if it can be classified as SHM.

### Step 2: Find the Velocity
To check if the motion is SHM, we first need to find the velocity. The velocity \( v \) is given by the derivative of \( y \) with respect to time \( t \):
\[
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