The displacement of a particle varies with time according to the relation `y=asinomegat+bcoasomegat`.

Options

A. The motion is oscillatory but not SHM
B. The motion is SHM with amplitude a+b
C. The motion is SHM with amplitude `a^(2)+b^(2)`
D. The motion is SHM with amplitude `sqrt(a^(2)+b^(2))`

Explanation

To solve the problem, we need to analyze the given displacement equation of a particle, which is:

\[ y = a \sin(\omega t) + b \cos(\omega t) \]

We want to determine whether this motion is simple harmonic motion (SHM) and, if so, find the amplitude.

### Step-by-Step Solution:

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