Q 11-13-137JEE MainJEE Main 2019 (8 Apr, Shift 2)Easy
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 $\dfrac{1}{1000}$ of the original amplitude is close to
Answer: (C) $20\ \text{s}$
10 oscillations take $10/5 = 2\ \text{s}$, so the amplitude halves every $2\ \text{s}$.
Since $2^{10} = 1024 \approx 1000$, the amplitude falls to $\frac1{1000}$ after about 10 halvings:
$$t \approx 10\times2 = 20\ \text{s}$$
Solution by Sreeraj P, M.Sc Physics