The displacement of a damped harmonic oscillator is given by $x ( \mathrm { t } ) = \mathrm { e } ^ { - 0.1 \mathrm { t } } \cos ( 10 \pi \mathrm { t } + \varphi )$. Here t is in seconds. The time taken for its amplitude of vibration to drop to half of its initial value is close to:\\
(1) 27 s\\
(2) 4 s\\
(3) 13 s\\
(4) 7 s