If two SHMs are represented by equations `y_(1) = 5 sin (2pi t + pi//6) and y_(2) = 5 [sin (3pi) + sqrt3 cos (3pi t)]`. Find the ratio of their amplitudes.

Explanation

To find the ratio of the amplitudes of the two simple harmonic motions (SHMs) given by the equations \( y_1 = 5 \sin(2\pi t + \frac{\pi}{6}) \) and \( y_2 = 5 \left[\sin(3\pi t) + \sqrt{3} \cos(3\pi t)\right] \), we can follow these steps:

### Step 1: Identify the amplitude of the first SHM
The first SHM is given by the equation:
\[ y_1 = 5 \sin(2\pi t + \frac{\pi}{6}) \]
In this equation, the amplitude \( A_1 \) is the coefficient of the sine function. Therefore,
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