Identify which of the following function represent simple harmonic motion.
(i) `Y = Ae^(I omega t)` (ii) `Y = a e^(- omega t)`
(iii) `y = a sin^(2) omega t` (iv) `y = a sin omega t + b cos omega t`
(v) `y = sin omega t + b cos 2 omega t`

Explanation

To determine which of the given functions represent simple harmonic motion (SHM), we need to check if they satisfy the condition for SHM: the second derivative of the displacement with respect to time should be proportional to the negative of the displacement itself. Mathematically, this is expressed as:

\[ \frac{d^2y}{dt^2} + \omega^2 y = 0 \]

Let's analyze each function step by step.

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