The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5 s . In another 10 s it will decrease to α times its original m - Physics MCQ JEE Main 2026 | ExamTest.live

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

Solution & Step-by-step Explanation

Amplitude of a damped oscillator is A (t) = A_{0} e^{- b t} .For t = 5 s : 0.9 A_{0} = A_{0} e^{- 5 b} \Rightarrow e^{- 5 b} = 0.9 .For total t = 5 + 10 = 15 s : A (15) = A_{0} e^{- 15 b} = A_{0} (e^{- 5 b})^{3} . α = (0.9)^{3} = 0.729 .

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

0.81

0.729

0.6

0.7

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