`x_(1) = 3 sin omega t`,`x_(2) = 4 cos omega t`
Find (i) amplitude of resultant SHM, (ii) equation of the resultant SHM.

Explanation

To solve the problem, we need to find the amplitude of the resultant simple harmonic motion (SHM) and the equation of the resultant SHM given the two equations \( x_1 = 3 \sin(\omega t) \) and \( x_2 = 4 \cos(\omega t) \).

### Step 1: Rewrite \( x_2 \) in terms of sine
We start by rewriting the cosine function in terms of sine:
\[ x_2 = 4 \cos(\omega t) = 4 \sin\left(\omega t + \frac{\pi}{2}\right) \]
This allows us to express both equations in terms of sine.
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