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AP EAMCET · PHYSICS · Oscillations

The mechanical energy of a damped oscillator becomes half of its initial energy in 4 seconds. In another \(t\) seconds its mechanical energy becomes \(12.5 \%\) of its initial mechanical energy. Then \(t=\)

  1. A \(4 \mathrm{~s}\)
  2. B \(8 \mathrm{~s}\)
  3. C \(12 \mathrm{~s}\)
  4. D \(16 \mathrm{~s}\)
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Answer & Solution

Correct Answer

(B) \(8 \mathrm{~s}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { at } \mathrm{t}=4, \mathrm{E}=\frac{\mathrm{E}_0}{2} \\ & E=E_0 e^{-b t / m} \Rightarrow \frac{E_0}{2}=E_0 e^{-\frac{4 b}{m}} \\ & \ln 2=\frac{4 b}{m} \\ & \frac{\mathrm{b}}{\mathrm{m}}=\frac{\ln 2}{4} \\ & \text { at } \mathrm{t}, \mathrm{E}=12.5 \%…

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