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Displacement of a damped harmonic oscillator is given by $x (t) = e^{- 0.1 t} \cos (10 π t + ϕ)$ where t is in seconds. The time taken for its amplitude of vibration to drop to half of its initial value is close to

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4 s

7 s

13 s

27 s

answer is B.

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Detailed Solution

A = A 0 e − 0.1 t ⇒ A 0 2 = A 0 e − 0.1 t ⇒ ln 2 = 0.1 t ⇒ t = 6.9 s

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