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A block of mass 500 g oscillates as a damped mass-spring system, so its amplitude diminishes over time. If the damping (decay) constant is 20 g/s, how long does it take for the oscillation amplitude to fall to one-half of its starting value? (Take ln 2 = 0.693)

1. 34.65 s
2. 17.32 s
3. 0.034 s
4. 15.01 s

Correct answer: 34.65 s

Solution

For a lightly damped oscillator the amplitude envelope is A(t) = A0 e^(-bt/2m). The time for it to halve depends only on m and b, not on the spring constant.

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