If two SHMs are repersented by `y_(1) = 10 sin (4 pi + pi//2)` and `y_(2) = 5 (sin 2 pi t +sqrt 8 cos 2 pi t)`, compare their amplitudes .

Explanation

To compare the amplitudes of the two simple harmonic motions (SHMs) represented by the equations \( y_1 = 10 \sin(4\pi t + \frac{\pi}{2}) \) and \( y_2 = 5 \left( \sin(2\pi t) + \sqrt{8} \cos(2\pi t) \right) \), we can follow these steps:

### Step 1: Identify the amplitude of the first SHM
The first SHM is given by:
\[ y_1 = 10 \sin(4\pi t + \frac{\pi}{2}) \]
The amplitude \( A_1 \) is the coefficient of the sine function, which is:
...