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Imagine that you have a mass m that you hang on a spring with spring constant...

Imagine that you have a mass m that you hang on a spring with spring constant k. The spring is setup to stay in a straight line (like wrapping it around a very light straight rod.) The equilibrium length of the spring is length l. Assume the motion takes place in a single plane. Write the Lagrangian, and the corresponding equations of motion, taking θ as the angle of the pendulum, and x as the distance from the equilibrium point of the spring.

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