Which of the following functions of time represents (a) periodic motion, (b) non-periodic motion and (c ) harmonic motion ?
find the period of each periodic motion. [`omega` is any positive constant]
(i) `sin 2omegat + cos 2omegat`
(ii) `cos omegat + 2 sin 2pit + 3 cos 3 pit`
(iii) `cos^(2)omegat`
(iv) `sin(2omegat + pi//3)`

Explanation

To solve the problem, we need to analyze each function of time given in the question and determine whether it represents periodic motion, non-periodic motion, or harmonic motion. We will also find the period of each periodic motion.

### Step-by-Step Solution:

**(i) Function: `sin(2ωt) + cos(2ωt)`**

1. **Identify the type of motion**:
- This function can be rewritten using the sine addition formula:
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