Which of the following funchtions of time represent (a) periodic and (b) non-periodic motion? Give the period for each of period motion. `(omega` is any positive constant )
(i) `sinomegat+cosomegat`
(ii) `sinomegat+cos2omegat+sin4omegat`
(iii) `e^(-omegat)` (iv) `logomegat`

Explanation

To solve the question regarding periodic and non-periodic functions, we will analyze each function provided and determine whether they are periodic or non-periodic. If they are periodic, we will also calculate their periods.

### Step-by-Step Solution:

1. **Function (i): \( \sin(\omega t) + \cos(\omega t) \)**
- Both sine and cosine functions are periodic with a period of \( 2\pi \).
- To find the period of the sum, we can express it as:
\[
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