Consider a pendulum consisting of a mass m in a gravitational field, with the (massless) pendulum...

Consider a pendulum consisting of a mass m in a gravitational field, with the (massless) pendulum arm being a spring of spring constant k and “resting length” b. The pendulum is confined to move in a plane as usual. Write the Lagrangian and find the equations of motion.

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genius_generous answered 2 years ago

A) Write the Lagrangian for a simple pendulum consisting of a point mass m suspended at...

A) Write the Lagrangian for a simple pendulum consisting of a point mass m suspended at the end of a massless string of length l. Derive the equation of motion from the Euler-Lagrange equation, and solve for the motion in the small angle approximation. B) Assume the massless string can stretch with a restoring force F = -k (r-r0), where r0 is the unstretched length. Write the new Lagrangian and find the equations of motion. C) Can you re-write the...

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