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Oscillations and Waves

  1. Dec 3, 2015 #1
    A suspension bridge oscillates with an effective force constant of mimetex.cgi?%5Cdisplaystyle%7B1.120%7D%5Ctimes%7B10%7D%5E%7B%7B%7B8%7D%7D%7D.gif N/m.

    (a) How much energy is needed to make it oscillate with an amplitude of 0.106 m?

    (b) If soldiers march across the bridge with a cadence equal to the bridge's natural frequency and impart mimetex.cgi?%5Cdisplaystyle%7B1.200%7D%5Ctimes%7B10%7D%5E%7B%7B%7B4%7D%7D%7D.gif J of energy each second, how many minutes does it take for the bridge's oscillations to go from 0.106 m to 0.530 m amplitude, assuming the bridge has no damping?

    RELEVANT EQUATIONS:
    For (a)
    Etot = (.05)(k)(xmax)^2

    For (b)
    not sure

    THE ATTEMPT AT THE SOLUTION:

    a)
    k = 1.120E8 N/m
    xmax^2 = .106 m

    Etot = (.05)(k)(xmax)^2 = (.05)(1.120E8)(.106) = 6.29E5 J
    This answer was correct on my webassign

    b) I'm very confused here. All I know is 6.29E5 J is the energy required to make it oscillate with an amplitude of .106 m
     
    Last edited by a moderator: Apr 17, 2017
  2. jcsd
  3. Dec 4, 2015 #2

    ehild

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    What is the energy when the bridge oscillates with 0.530 m amplitude?
    The soldiers impart mimetex.cgi?%5Cdisplaystyle%7B1.200%7D%5Ctimes%7B10%7D%5E%7B%7B%7B4%7D%7D%7D.gif J of energy each second to the bridge. How long time is needed that the bridge get the new energy?
     
    Last edited by a moderator: Apr 17, 2017
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