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A particle of mass m moves in one dimension subject to the potential V=(a)/(sin^2((x)/(40))) Obtain an integral expression for Hamilton's characteristic function. Under what conditions can action-ingle variables be used? Assuming these are met, find the frequency of oscillation by the action-angle method. (The integral for J can be evaluated by ma. manipulating the integrand so that the square root appears in the donominatcal Check your result in the limit of oscillations of small amplitude. | N
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