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Two simple harmonic motions of angular frequency 100 and 1000 rad s⁻¹ have the same displacement amplitude. The ratio of their maximum accelerations is:

1. 1 : 10
2. 1 : 10²
3. 1 : 10³
4. 1 : 10⁴

Correct answer: 1 : 10²

Solution

The maximum acceleration in SHM is given by a_max = ω²A, where ω is the angular frequency and A is the amplitude. Since the amplitudes are the same, the ratio of maximum accelerations is proportional to the square of the angular frequencies: (1000/100)² = 10². Thus, the ratio is 1:10².

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