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JEE Main 2021 (16 Mar, Shift 2) · Damped, Forced Oscillations & Superposition

Damped, Forced Oscillations & Superposition question from JEE Main 2021 (16 Mar, Shift 2)

Q7JEE Main 2021 · 16 MAR · SHIFT 2Medium

Damped, Forced Oscillations & Superposition

Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass = 500g, Decay constant = 20 g/s then how much time is required for the amplitude of the system to drop to half of its initial value? (ln 2 = 0.693)

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Answer: (b)

$A = A_0 e^{-bt/2m}$ ; for $A = A_0/2$ : $t = \frac{2m \ln 2}{b}$ .
$t = \frac{2 \times 500 \times 0.693}{20}$ (both in grams, units cancel).
$t = 34.65\ \text{s}$ .
So the answer is (b) 34.65 s.

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