Which of the following functions of time represent (a) simple harmonic motion and (b) periodic but not simple harmonic motion? Give the period for each case.
(i)` sinomegat-cosomegat` (ii) `sin^(2)omegat` (iii) `cosomegat+2sin^(2)omegat`

Explanation

To determine which of the given functions represent simple harmonic motion (SHM) and which are periodic but not SHM, we will analyze each function step by step.

### Step 1: Analyze the first function \( x_1(t) = \sin(\omega t) - \cos(\omega t) \)

1. **Combine the terms**: We can express the function in a single sine function form.
\[ x_1(t) = \sin(\omega t) - \cos(\omega t) = \sqrt{2} \left( \frac{1}{\sqrt{2}} \sin(\omega t) - \frac{1}{\sqrt{2}} \cos(\omega t) \right) \]
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