Does `cos omegat +sin2 omega t +cos 4 omega t ` represent periodic motion ? If yes, then find the period`( omega` is any positive constant) .
Hint `:` ( Each term represents a periodic function with different angular freuency . Find the smallest interval of time after which the sum of three terms repeats ) .

Explanation

To determine whether the function \( f(t) = \cos(\omega t) + \sin(2 \omega t) + \cos(4 \omega t) \) represents periodic motion, we need to analyze the periodicity of each term in the function.

### Step 1: Identify the periods of each term
1. **For \( \cos(\omega t) \)**:
- The period \( T_1 \) is given by:
\[ T_1 = \frac{2\pi}{\omega} \]
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