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Homework Help: SHO of Water Sloshing in a Container

  1. Sep 26, 2012 #1
    1. The problem statement, all variables and given/known data

    Consider a rectangular container, dimensions L x b, filled to level h with water. Water sloshes at low amplitude, y0 << h so that its surface remains always flat. Assuming the water has a density of δ, show that the potential energy is

    [itex] U(y) = \frac{1}{6} b δ g L y^2 [/itex]

    2. Relevant equations
    [itex] F = ma [/itex]

    [itex] U = \frac{1}{2} k x^2 [/itex]

    3. The attempt at a solution

    Since F = ma = kx = mgh, I know that k = mg because x and h in this case are y0. And m is bLδ meaning that k = bLδg.

    So integrating ky0 to get the potential energy I get

    [itex] U(y) = \frac{1}{2} b δ g L y^2 [/itex]

    but the answer has a fraction of 1/6, where did the extra 1/3 come from?
  2. jcsd
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