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 analyze each function based on the criteria for SHM. A function represents SHM if it can be expressed in the form of a sine or cosine function, or if it satisfies the differential equation of SHM, which is:

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

Let's analyze each function step by step:

### Step 1: Analyze the first function
**Function (i):** \( Y = A e^{i \omega t} \)
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