The displacement of a damped oscillator is $x(t)=\exp$ $(-0.2 \mathrm{t}) \cos (3.2 \mathrm{t}+\Phi)$ where $t$ is time in second. The time required for the amplitude of the oscillator to become $\frac{1}{e^{1.2}}$ times its initial amplitude is

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Aicharya · Accepted Answer

For damped oscillator, $x=\mathrm{e}^{-0.2 \mathrm{t}} \cos (3.2 \mathrm{t}+\phi)$ $\begin{aligned} & 	herefore 	ext { Amplitude, } \mathrm{A}=\mathrm{e}^{-0.2 \mathrm{t}} \ & 	ext { For } \mathrm{A}=1 	imes \frac{1}{\mathrm{e}^{1.2}} \ & \frac{1}{\mathrm{e}^{1.2}}=\mathrm{e}^{-0.2 \mathrm{t}} \Rightarrow 0.2 \mathrm{t}=1.2 \ & 	herefore \mathrm{t}=6 \mathrm{~s}\end{aligned}$

The displacement of a damped oscillator is $x(t)=\exp$ $(-0.2 \mathrm{t}) \cos (3.2 \mathrm{t}+\Phi)$ where…

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