Two SHM's are represented by `y_(1) = A sin (omega t+ phi), y_(2) = (A)/(2) [sin omega t + sqrt3 cos omega t]`. Find ratio of their amplitudes.

Explanation

To find the ratio of the amplitudes of the two simple harmonic motions (SHMs) given by the equations \( y_1 = A \sin(\omega t + \phi) \) and \( y_2 = \frac{A}{2} \left[ \sin(\omega t) + \sqrt{3} \cos(\omega t) \right] \), we can follow these steps:

### Step 1: Identify the amplitude of the first SHM
The first SHM is given by:
\[ y_1 = A \sin(\omega t + \phi) \]
In this equation, the amplitude \( A_1 \) is simply \( A \).
...