The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5 s. In another 10 s it will decrease to α times its original magnitude, where α equals (a) 0.7 (b) 0.81 (c) 0.729 (d) 0.6

Answer: (c). A = A₀ e-γ t: amplitude falls by factor 0.9 in every 5 s. Total time 5 + 10 = 15 s = three 5 s intervals. α = (0.9)³ = 0.729. So the answer is (c) 0.729.

The amplitude of a damped oscillator decreases to 0.9 times its… | JEE Main 2013

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Damped, Forced Oscillations & Superposition

The amplitude of a damped oscillator decreases to $0.9$ times its original magnitude in $5\text{ s}$ . In another $10\text{ s}$ it will decrease to $\alpha$ times its original magnitude, where $\alpha$ equals

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Answer: (c)

$A = A_0 e^{-\gamma t}$ : amplitude falls by factor 0.9 in every 5 s.
Total time $5 + 10 = 15\ \text{s}$ = three 5 s intervals.
$\alpha = (0.9)^3 = 0.729$ .
So the answer is (c) 0.729.

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