JEE PYQ: Waves And Sound Question 30
Question 30 - 2019 (10 Apr Shift 1)
The displacement of a damped harmonic oscillator is given by $x(t) = e^{-0.1t}\cos(10\pi t + \phi)$. Here $t$ is in seconds. The time taken for its amplitude of vibration to drop to half of its initial value is close to :
(1) 4 s
(2) 7 s
(3) 13 s
(4) 27 s
Show Answer
Answer: (2)
Solution
Amplitude of vibration at time $t = 0$ is given by
$A = A_0 e^{-0.1 \times 0} = 1 \times A_0 = A_0$
Also at $t = t$, if $A = \frac{A_0}{2}$
$\Rightarrow \frac{1}{2} = e^{-0.1t}$
$t = 10\ln 2 \approx 7$ s
BETA
