The amplitude of a damped oscillator becomes (1/3)rd of original amplitude in 2 seconds. If its amplitude after 6 second become (1/n) times the original amplitude, the value of n is ( n is non zero integer) (a) 9 (b) 3 (c) 81 (d) 27

Answer: (d). Damped amplitude A = A₀ e-γ t, so in equal time intervals it falls by the same factor. In 2 s: A/A₀ = 1/3. 6 s = three 2 s intervals: A/A₀ = (1/3)³ = 1/27. So the answer is (d) n = 27.

The amplitude of a damped oscillator becomes (1/3)rd of original… | MHT CET 2025 (23 Apr, Shift 1)

Q1MHT CET 2025 · 23 APR · SHIFT 1Medium

Damped, Forced Oscillations & Superposition

The amplitude of a damped oscillator becomes $\left(\frac{1}{3}\right)^{\text{rd}}$ of original amplitude in 2 seconds. If its amplitude after 6 second become $\left(\frac{1}{n}\right)$ times the original amplitude, the value of $n$ is ( $n$ is non zero integer)

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Answer: (d)

Damped amplitude $A = A_0 e^{-\gamma t}$ , so in equal time intervals it falls by the same factor.
In 2 s: $A/A_0 = \frac{1}{3}$ .
6 s = three 2 s intervals: $A/A_0 = \left(\frac{1}{3}\right)^3 = \frac{1}{27}$ .
So the answer is (d) $n = 27$ .

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