Problem 6b) A ring of mass m is constrained to move along a massless rigid wire, as shown. The wire rotates in the my plane at a constant angular velocity 0.) such that (9(73) = wt, rr(0) = l, and 6(0) = 0. Note: gravity is present and acts downward (in the y direction). axis (i) Determine an expression for the Lagrangian. Then determine Lagrange's equation of motion for the 'r coordinate, but do not solve the equation of motion. (ii) Determine the conjugate momentum for the r coordinate and call it p... Then deter mine an expression for the Hamiltonian as a function of 7", pr, and 15. (iii) Determine the full derivative of H with respect to time, dH/dt. Is it constant? (iv) Show that H is not equal to the total energy. RX - JL P - JL = mr Now Hamiltonian H = Px 4x - L + mas sine 2 m 2 p 2 A - m 2m + mas sine 2my H ( q p, t ) = - mas sin ( wt ) 2 m