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Question

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


A
2×3
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B
23
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C
32
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D
3×22
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Solution

The correct option is B $$2^3$$
Amplitude of damped oscillator
$$A=A_0e^{- \lambda t} ; \lambda =constant, t=time$$
For $$t=1\ min. \dfrac{A_0}{2}=A_0 e^{- \lambda t} \Rightarrow e^{\lambda}=2$$
For $$t=3\ min.\ A=A_0e^{- \lambda \times 3 }=\dfrac{A_0}{(e^{\lambda})^3}=\dfrac{A_0}{2^3}$$
$$\Rightarrow X=2^3$$

Physics

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