JEE Mains · Physics · STD 11 - 13. oscillations
A damped harmonic oscillator has a frequency of \(5\) oscillations per second. The amplitude drops to half its value for every \(10\) oscillations. The time it will take to drop to \(\frac{1}{1000}\) of the original amplitude is close to .... \(s\)
- A \(10\)
- B \(100\)
- C \(50\)
- D \(20\)
Answer & Solution
Correct Answer
(D) \(20\)
Step-by-step Solution
Detailed explanation
\(A=A_{0} e^{-\gamma t}\) \(A=\frac{A_{0}}{2}\) after \(10\) oscillations \(\because\) After 2 seconds \(\frac{A_{0}}{2}=A_{0} e^{-\gamma(2)} \quad ; \quad 2=e^{2 \gamma}\) \( \ell n 2=2 \gamma \quad ; \quad \gamma=\frac{\ell n 2}{2}\) \(\because A=A_{0} e^{-\gamma t}\)…
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