Damped Harmonic Oscillator Amplitude Decay – Rankers Physics

Energy in SHM: Practice Problem & Solution

For the damped oscillator, if time taken for its amplitude of vibrations to drop to half of its initial value is \(T\) then time taken for amplitude to drop to one eighth amplitude is
t = 2T
t = 3T
t = 4T
t = T/2

Solution Explained:

To solve this problem, we apply the core principles of Energy in SHM. Understanding the underlying formula is key to arriving at the correct answer below:

Amplitude decays exponentially as \(A = A_0 e^{-\gamma t}\). Since it halves in time \(T\), to drop to \(1/8 = (1/2)^3\) of its initial value, it takes exactly \(3T\).

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