TS EAMCET · Physics · Oscillations
If the amplitude of a damped harmonic oscillator becomes half of its initial amplitude in a time of 10 s, then the time taken for the mechanical energy of the oscillator to become half of its initial mechanical energy is
- A 2.5 s
- B 20 s
- C 10 s
- D 5 s
Answer & Solution
Correct Answer
(D) 5 s
Step-by-step Solution
Detailed explanation
\(A(t) = A_0 e^{-\beta t}\) \(E(t) = E_0 e^{-2\beta t}\) \(A(10) = A_0/2 \Rightarrow 1/2 = e^{-10\beta}\) \(E(t) = E_0/2 \Rightarrow 1/2 = e^{-2\beta t}\) \(e^{-2\beta t} = e^{-10\beta}\) \(t = 5\) s
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