The mass mi moves on a smooth horizontal plane. m2 moves vertically under the force of gravity and the spring. Using polar coordinates r, θ for mi, l for m2, and taking b for the total length of the string plus the unstretched length of the spring, find
(a) the Lagrangian of the system
(b) the equations of motion for mass m1 in terms of the radial coordinate r, and for m2 in terms of l
(c) at any given angular velocity θ there will be "equilibrium" values for the positions of m1 and m2. Find these values ro and lo.
