First slide
Damped and forced oscillations
Question

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?

Difficult
Solution

A=A0ebt2mA02=A0ebt2mbt2m=ln2=0.693t=2mb×0.693t=2×50020×0.693=50×0.693=34.65 sec.

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