A child stops pumping on a swing. Its amplitude is 40 cm, and it falls to 20 cm in 15 s…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A child stops pumping on a swing. Its amplitude is , and it falls to in . (a) What is the amplitude after the child stops? (b) What fraction of the starting energy is left after ?
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
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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) holds four times . So the amplitude halves four times: .
(b) After the amplitude is half, so the energy is of the start, .
Watch out. The amplitude does not fall by in every . That would bring it to zero after .
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