3 A bead of mass m slides without iction on a rotating circular hoop. The hoop is forced to rotate about a vertical axis along its diameter at a constant angular velocity 2. The position of the bead can be described by the angle 6, which is the angle that a line running between the center of the hoop and the bead makes with the vertical. A) Show that the Lagrangian for the system is ma² L=T-V=- B) Find the Hamiltonain. C) Write Hamiltons equations of motion. g Good Luck J - (²+0² sin² e) - mga(1 - cos 6) ads 171 La _=ma² (6²+ 2² simp) - myo

3 A bead of mass m slides without iction on a rotating circular hoop. The hoop is forced to rotate about a vertical axis along its diameter at a constant angular velocity 2. The position of the bead can be described by the angle 6, which is the angle that a line running between the center of the hoop and the bead makes with the vertical. A) Show that the Lagrangian for the system is ma² L=T-V=- B) Find the Hamiltonain. C) Write Hamiltons equations of motion. g Good Luck J - (²+0² sin² e) - mga(1 - cos 6) ads 171 La _=ma² (6²+ 2² simp) - myo