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

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Q. The amplitude of a damped oscillator decreases to $0.9$ times its original magnitude is $5\, s$. In another $10\, s$ it will decrease to a times its original magnitude, where $\alpha$ equals

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Solution:

Amplitude decreases exponentially. In 5 s it remains 0.9 times. Therefore in total 15 s it will remains (0.9) (0.9) Answer is 4. (0.9) = 0.729 times its original value.