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:

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:, 50 s, 100 s, 20 s, 10 s

MARKS App · Accepted Answer

f = 5 So, T = 1 5 Time taken for amplitude to drop to half: 10 T = 10 5 = 2 s Now, A 0 1000 = A 0 ( 2 ) t 2 ( 2 ) t 2 = 1000 t 2 l o g 2 = 3 t = 6 l o g 2 ≈ 20 s

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