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The amplitude of a pendulum executing simple harmonic motion falls to 1/3 the original value after 100 oscillations. The amplitude falls to S times the original value after 200 oscillations, where S is:

1. 1/9
2. 2/3
3. 1/2
4. 1/6

Correct answer: 1/9

Solution

The amplitude of a damped harmonic oscillator decreases exponentially with the number of oscillations. If the amplitude becomes 1/3 after 100 oscillations, after another 100 oscillations (total 200), it will reduce by the same factor, i.e., (1/3) × (1/3) = 1/9.

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