If two `S.H.M.'s` are represented by equation `y_(1) = 10 "sin" [3pit+(pi)/(4)]` and `y_(2) = 5[sin(3pit)+sqrt(3)cos(3pit)]` then find the ratio of their amplitudes and phase difference in between them.
Text Solution
AI Generated Solution
To solve the problem, we need to analyze the two equations of simple harmonic motion (SHM) given:
1. \( y_1 = 10 \sin \left(3\pi t + \frac{\pi}{4}\right) \)
2. \( y_2 = 5 \left[\sin(3\pi t) + \sqrt{3} \cos(3\pi t)\right] \)
### Step 1: Identify the Amplitudes
The amplitude of the first SHM \( y_1 \) is straightforward:
- From \( y_1 = 10 \sin \left(3\pi t + \frac{\pi}{4}\right) \), the amplitude \( A_1 = 10 \).
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