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JEE Main 2017 (9 Apr, Shift 1) · Damped, Forced Oscillations & Superposition

Damped, Forced Oscillations & Superposition question from JEE Main 2017 (9 Apr, Shift 1)

Q13JEE Main 2017 · 9 APR · SHIFT 1Medium

Damped, Forced Oscillations & Superposition

A block of mass 0.1 kg is connected to an elastic spring of spring constant 640 Nm−1 and oscillates in a damping medium of damping constant 10−2 kg s−1. The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to:

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Answer: (d)

$A = A_0 e^{-bt/2m}$ , so energy $E \propto A^2$ gives $E = E_0 e^{-bt/m}$ .
$E = E_0/2 \Rightarrow t = \frac{m \ln 2}{b}$ .
$t = \frac{0.1 \times 0.693}{10^{-2}} = 6.93\ \text{s} \approx 7\ \text{s}$ .
So the answer is (d) 7 s.

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