Q132 / 160 · AP EAMCET 2024 (19 May Shift 2) · Physics

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

  • A
    3s
  • Correct answer
    B
    6s
  • C
    2s
  • D
    8s

Solution

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

Hence, the correct answer is option: 'B'.

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