First slide

Damped oscillation

Question

The amplitude of a damped oscillator becomes $\frac{1}{27} th$ of its initial value after 6 minutes. Its amplitude after 2 minutes is

Easy

A

$\frac{A_{0}}{3}$
B

$\frac{A_{0}}{9}$
C

$\frac{A_{0}}{54}$
D

$\frac{A_{0}}{81}$

Solution

$For damped oscillator A = A_{0} e^{- bt}$
$Here \frac{A_{0}}{27} = A_{0} e^{- 6 b}, A_{2} = A_{0} e^{- 2 b} = A_{0} {[e^{- 6 b}]}^{\frac{1}{3}}$

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