A 0.25 kg bob oscillates in oil. The oil pushes on it with a damping force -bv, where b = 0.050…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A bob oscillates in oil. The oil pushes on it with a damping force , where . (a) How long does its amplitude take to fall to half? (b) How long does its energy take to fall to half?
Need a reminder? The key ideaShow
With a damping force , the amplitude falls as and the energy as . A periodic force drives the body at its own frequency; the amplitude is largest at resonance, when the driving frequency equals the natural frequency.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
(a) Amplitude. We want , so from :
(b) Energy. From : .
Check. The energy halves in half the time, because it goes as the square of the amplitude.
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