Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass=500g, Decay constant=20 g/s then how much time is required for the amplitude of the system to drop to half of its initial value?

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17.32s

34.65s

0.034s.

15.01s.

answer is B.

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Detailed Solution

A=A0e−bt2m⇒A02=A0e−bt2m⇒bt2m=ln⁡2=0.693⇒t=2mb×0.693⇒t=2×50020×0.693=50×0.693=34.65 sec.

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