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Langrangian Generalized Coordinates

Consider the pendulum of figure 7.4, suspended inside a railroad car, but suppose that the can is oscillating back and forth, so that the point of suspension has position x=Acos(wt), y=0. Use the angle Φ as the generalized coordinate and write down the equations that give the Cartesian coordinates of the bob in terms of Φ and vice versa.

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Detailed calculations in attached documents.