A damped oscillator’s amplitude falls to 0.9 of its initial value in 5 s. After an additional 10 s, what fraction of the initial amplitude will it have, if the factor is denoted by α?

0.7
0.81
0.729
0.6

Correct answer: 0.729

Solution

Amplitude decays as A = A0*e^(-bt). In each 5 s interval it multiplies by 0.9. After 15 s total (3 intervals): (0.9)^3 = 0.729 of the initial amplitude.

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