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>> $The amplitude of a damped oscillator bec$

Question

The amplitude of a damped oscillator becomes half on one minute. The amplitude after 3 minute will be $\frac{1}{X}$ times the original, where $X$ is

A

$2 \times 3$

B

$2^{3}$

C

$3^{2}$

D

$3 \times 2^{2}$

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Solution

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Correct option is B)

Amplitude of damped oscillator
$A = A_{0} e^{- λ t}; λ = c o n s t a n t, t = t i m e$
For $t = 1 m i n . \frac{A _{0}}{2} = A_{0} e^{- λ t} \Rightarrow e^{λ} = 2$
For $t = 3 m i n . A = A_{0} e^{- λ \times 3} = \frac{A _{0}}{( e ^{λ} ) ^{3}} = \frac{A _{0}}{2 ^{3}}$
$\Rightarrow X = 2^{3}$

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