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Stuck on Wave Motion Problem

  1. Dec 30, 2004 #1
    I've looked at the following problem several times and have gotten stuck.

    The Problem
    An earthquake-produced suface wave can be approximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground?

    My Thoughts So Far
    To leave the ground acceleration must be 9.8 m/s^2. The equation of motion is x = A cos 2 Pi f t, where A is amplitude, f is frequency and t is time. I'm not sure how go from this point to get the equation for acceleration. :confused:

    What's the next step?
  2. jcsd
  3. Dec 30, 2004 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Find the second derivative of x with respect to t, and that's your acceleration.

    Then, you want to find the maximum value that this can take, which is easy, since trigonometric functions are bounded.
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