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 resulting two coupled 2 nd -order differential equations as four coupled 1 st - order differential equations (Hint: Let v=dr/dt and ω = dϑ/dt).

Expert Solution

genius_generous answered 2 years ago

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