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The amplitude of a damped oscillator falls to 0.9 of its initial value in 5 s. After a further 10 s, the amplitude becomes 'a' times its original value. Find a.

1. 0.81
2. 0.729
3. 0.6
4. 0.7

Correct answer: 0.729

Solution

Amplitude decays as A0*e^(-b*t). In 5 s, factor = 0.9. Total time 5 + 10 = 15 s = three 5-s intervals, so factor = 0.9³ = 0.729. Thus a = 0.729.

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