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Question 5 (20pts). A system of masses and pulleys is given below. The pulley 1 is fixed to a ceiling and free to rotate about its axis. The mass m3 is attached to the pulley 2 over the pulley 1 with a string of constant length l2 while the mass m1 and m2 are attached to each other with a string of constant length l1 over the pulley 2 as seen in the figure. Assume that the pulleys are massless and there is no loss of energy due to friction. (a) Construct the Lagrangian of the system. (b) Construct the Hamiltonian of the system. (c) Find the Hamilton's equations of motion. (d) Find the acceleration of mass m3 using Hamilton's equations.

          Question 5 (20pts). A system of masses and pulleys is given below. The pulley 1 is fixed to a ceiling and free to rotate about its axis. The mass m3 is attached to the pulley 2 over the pulley 1 with a string of constant length l2 while the mass m1 and m2 are attached to each other with a string of constant length l1 over the pulley 2 as seen in the figure. Assume that the pulleys are massless and there is no loss of energy due to friction.
(a) Construct the Lagrangian of the system.
(b) Construct the Hamiltonian of the system.
(c) Find the Hamilton's equations of motion.
(d) Find the acceleration of mass m3 using Hamilton's equations.

Question 5 (20pts). A system of masses and pulleys is given below. The pulley 1 is fixed to a ceiling and free to rotate about its axis. The mass m3 is attached to the pulley 2 over the pulley 1 with a string of constant length l2 while the mass m1 and m2 are attached to each other with a string of constant length l1 over the pulley 2 as seen in the figure. Assume that the pulleys are massless and there is no loss of energy due to friction.
(a) Construct the Lagrangian of the system.
(b) Construct the Hamiltonian of the system.
(c) Find the Hamilton's equations of motion.
(d) Find the acceleration of mass m3 using Hamilton's equations.

Added by Jay B.

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