Which of the following functions of time represent (a) simple harmonic (b) periodic but not simple harmonic and (c ) non periodic motion? Give period for each case of periodic motion `(omega` is nay positive constant)
(1) `Sin^(3) omegat` (2) `3cos (pi//4 -2 omegat)`
(3) `cos omegat +cos 3 omegat + cos 5 omegat`
(4) `e^(-omega^(2)t^(2))` (5) `1 + omegat +omega^(2) t^(2)`

Explanation

To solve the problem, we will analyze each function of time given in the question to determine whether it represents simple harmonic motion (SHM), periodic but not SHM, or non-periodic motion. We will also find the period for each case of periodic motion.

### Step-by-Step Solution:

1. **Function: \( \sin^3(\omega t) \)**
- We can use the trigonometric identity:
\[
\sin^3(x) = \frac{3\sin(x) - \sin(3x)}{4}
...