Answer Happy

please answer part e, f and g
A rope of length a slides under constant gravity g from a tilted frictionless tabletop which makes an angle o to horizontal as shown in the figure below. The rope has a total mass m. The tabletop is completely fixed throughout the motion. horizontal line х = 2 (a) Write down the Lagrangian of the rope in term of x. [5pt] (b) Find the generalized momentum. [5pt] (c) Write down the Hamiltonian of the rope. [5pt] (d) Find the Hamilton equations of motion of the rope. [5pt] (e) If 0 = " and the rope is initially released from rest with the lower end at the edge of the tabletop. Find the time, T1, at which the upper end of the rope reaches the edge of the table. [5pt] (f) For 0 = 0, consider the rope is initially (t = 0) moving towards the edge of the table with speed v(0) = vo and the right end of the rope is at the edge of the table, x(0) = 0. Solve the Hamilton equation of motion to find x(t). [10pt] (g) Continue on (f). Take a = 1 and v. = 1. Find the time, T2, at which the left end of the rope reaches the edge of the table. [5pt] =