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A light footbridge sways sideways with a natural period of 0.52 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 light footbridge sways sideways with a natural period of . A group of soldiers marches across it in step, at steps each minute. (a) Find the frequency of their steps. (b) Find the natural frequency of the bridge. (c) Why are soldiers told to break step on such a bridge?
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) Steps. .
(b) The bridge. .
(c) Why break step? The two frequencies are almost equal. Every step pushes the bridge at the right moment, so its sway grows larger and larger. That is resonance. When the soldiers walk out of step, their pushes come at random moments and do not add up.
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