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The displacement of a damped harmonic oscillator is given by \( x(t)=e^{-0.1 t} \cos (10 \pi t+\phi) \). Here \( t \) is in seconds. The
\( \mathrm{P} \) time taken for its amplitude of vibration to drop to half of its initial value is close to
[JEE (Main) 2019]
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(a) \( 13 s \)
(b) \( 7 \mathrm{~s} \)
(c) \( 4 s \)
(d) \( 27 s \)
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