The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5s. In another 10 s it will decrease to α times its original magnitude, where α equals :

Engineering

Physics

Damped Oscillation

Question

0.81

0.729

0.7

0.6

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A = A₀e^–rt

0.9A₀ = A₀e^{–r × 5}

αA₀ = A₀e^{–r × 15}

⇒α = (0.9)³ = 0.729

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