# Correlating frequency of oscillation to shape of wave

A rectangular body of water undergoes oscillation at a frequency of $\sqrt{\frac{12hg}{L^2}}$ where h is the depth and L is the width of the larger side of the rectangular body of water. How can you derive this frequency by showing a parabolic trajectory of $y = \frac{6h}{L^2}x^2$ where $x$ and $y$ are the coordinates measured from the equilibrium position?

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Please check my edits to see if you agree. In particular it appears the frequency is the desired result, not an input, and the parabolic trajectory is a step along the way. Do you expect us to start from the equation of motion? –  Ross Millikan Feb 7 '11 at 13:35
Yes this is all correct –  PICyourBrain Feb 7 '11 at 17:41
If you preface a comment with @Ross: I will get a notification of your response. You also get a notification of all comments to your own questions. So what is your equation of motion? –  Ross Millikan Feb 7 '11 at 17:59