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AP EAMCET · PHYSICS · Oscillations

The amplitudes of a damped harmonic oscillator after 2 and 4 seconds are \(A_1\) and \(A_2\) respectively. If the initial amplitude of the oscillator is \(\mathrm{A}_0\), then

  1. A \(\mathrm{A}_1=\sqrt{\mathrm{A}_0 \mathrm{~A}_2}\)
  2. B \(\mathrm{A}_2=\sqrt{\mathrm{A}_0 \mathrm{~A}_1}\)
  3. C \(\mathrm{A}_0=\sqrt{\mathrm{A}_1 \mathrm{~A}_2}\)
  4. D \(\mathrm{A}_1=\frac{\mathrm{A}_0+\mathrm{A}_2}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\mathrm{A}_1=\sqrt{\mathrm{A}_0 \mathrm{~A}_2}\)

Step-by-step Solution

Detailed explanation

In damping harmonic oscillator, amplitude \[ \begin{aligned} & A=A_0 e^{-b t} \\ & \therefore A_1=A_0 e^{-b \times 2} \Rightarrow \frac{A_1}{A_0}=e^{-2 b} \end{aligned} \] And…