• # question_answer The displacement of a damped harmonic oscillator is given by $x(t)={{e}^{-01.1t}}\cos (10\pi t+\phi ).$Here t is in seconds. The time taken for its amplitude of vibration to drop to half of its initial value is close to: [JEE Main 10-4-2019 Morning] A) 13 s                 B) 7 sC) 27 s                 D) 4 s

$A={{A}_{0}}{{e}^{-0.1t}}=\frac{{{A}_{0}}}{2}$ $\ln 2=0.1t$           $t=10\ln 2=6.93\approx 7\sec$