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Homework due on Nov 18th for Classical Mechanics Fetter-Walecka – Chapter 6 – 15 3 dimensional oscillator Goldstein Chapter 10 problem 15 A particle of mass m moves in a one dimension subject to the potential V (x ) = a x sin 2 x0 Obtain an integral expression for Hamilton’s characteristic function. Under what conditions can action-angle 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 manipulating the integrand so that the square root appears in the denominator). Check your results in the limit of oscillations of small amplitude. 30 25 20 15 10 5 0.5 1.0 1.5 2.0 2.5 3.0