`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:

1. \( x_1 = 3 \sin(\omega t) \)
2. \( x_2 = 4 \cos(\omega t) \)

### Step 1: Convert \( x_2 \) to sine form
To combine the two equations, we need both to be in terms of sine. We can convert the cosine function into sine using the identity:
\[
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