A 4. A uniform bar of mass M and length 2l is suspended from one end by a spring of force constant k. The bar can swing freely only in the x, y plane, and the spring is constrained to move only in the vertical (ie, y) direction. a) Set up the equations of motion in the La- grangian formulation. (You do not need to solve them.) b) Find the Hamiltonian for the system and Hamilton's equations of motion for the system. g Y 0