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).