Question:
A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for every 10 oscillations. The time it will take to drop to \(1/1000\) of the original amplitude is close to :-
A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for every 10 oscillations. The time it will take to drop to \(1/1000\) of the original amplitude is close to :-
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Ten oscillations at 5 oscillations per second take 2 s per halving of the amplitude; you need \(\log_2 1000 \approx 10\) halvings.
Updated On: Nov 5, 2026
- \(100\ \mathrm{s}\)
- \(10\ \mathrm{s}\)
- \(20\ \mathrm{s}\)
- \(50\ \mathrm{s}\)
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The Correct Option is C
Solution and Explanation
Time for 10 oscillations \(= \frac{10}{5} = 2\ \mathrm{s}\). So the amplitude halves every 2 s: \(A = A_0\left(\frac{1}{2}\right)^{t/2}\).
Require \(A = \frac{A_0}{1000}\): \(2^{t/2} = 1000\).
\(\frac{t}{2} = \log_2 1000 = \frac{3}{0.301} \approx 9.97 \approx 10\).
\(t \approx 2\times10 = 20\ \mathrm{s}\).
Answer: (3) \(20\ \mathrm{s}\)
Require \(A = \frac{A_0}{1000}\): \(2^{t/2} = 1000\).
\(\frac{t}{2} = \log_2 1000 = \frac{3}{0.301} \approx 9.97 \approx 10\).
\(t \approx 2\times10 = 20\ \mathrm{s}\).
Answer: (3) \(20\ \mathrm{s}\)
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