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JEE Main 2019 (8 Apr, Shift 2) · Damped, Forced Oscillations & Superposition

Damped, Forced Oscillations & Superposition question from JEE Main 2019 (8 Apr, Shift 2)

Q11JEE Main 2019 · 8 APR · SHIFT 2Medium

Damped, Forced Oscillations & Superposition

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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Answer: (c)

Period $= \frac{1}{5}\ \text{s}$ , so 10 oscillations take 2 s: amplitude halves every 2 s.
$\frac{1}{1000} \approx \frac{1}{1024} = \left(\frac{1}{2}\right)^{10}$ , so 10 halvings are needed.
$t = 10 \times 2 = 20\ \text{s}$ .
So the answer is (c) 20 s.

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