A triple pendulum consists of three light rods supporting 3 pendulums bobs of equal mass m....

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A triple pendulum consists of three light rods supporting 3 pendulums bobs of equal mass m. The length of the top pendulum is 2L, and the lengths of the second and third are both L. The mass of the rods and any friction in the joints can be ignored. 2L e m (i) Derive the equations of motion for free oscillations of the system. You can choose your method, but put the final result in the form = (),i=1,2,3. (iii) Apply the assumption that 0, 02, and 03 are small to linearize the equations. With the linearized system, determine the eigenvalues in terms of L and m. For each, determine the eigenvectors. (ii) The system is put into motion from rest at 0 = 0, 02-03 = 0. With these initial conditions determine the motion through one period of the lowest frequency mode. A triple pendulum consists of three light rods supporting 3 pendulums bobs of equal mass m. The length of the top pendulum is 2L, and the lengths of the second and third are both L. The mass of the rods and any friction in the joints can be ignored. 2L e m (i) Derive the equations of motion for free oscillations of the system. You can choose your method, but put the final result in the form = (),i=1,2,3. (iii) Apply the assumption that 0, 02, and 03 are small to linearize the equations. With the linearized system, determine the eigenvalues in terms of L and m. For each, determine the eigenvectors. (ii) The system is put into motion from rest at 0 = 0, 02-03 = 0. With these initial conditions determine the motion through one period of the lowest frequency mode.