Categorise the following function of time `: sin omega t + sin 5 omega t ` as
(a) S.H.M.
(b) Periodic but no S.H.M. .Also give the period.
Hint `:` Find the smallest interval of time after which the sum of 2 terms repeats

Explanation

To categorize the function \( f(t) = \sin(\omega t) + \sin(5\omega t) \) as either Simple Harmonic Motion (S.H.M) or periodic but not S.H.M, we will follow these steps:

### Step 1: Identify the periods of the individual functions
The period \( T \) of a sine function \( \sin(\omega t) \) is given by the formula:
\[ T = \frac{2\pi}{\omega} \]
For the first term \( \sin(\omega t) \):
...