In the system shown below, a uniform disk (mass m, radius r) rolls without slipping with a spring k attached at its center. The top of the disk is attached to a massless rod of length L, which is pinned at a distance of L/3. The rod is also attached to a spring k and damper c equally spaced at intervals of L/3 as shown. Assume small oscillations. O corresponds to the rotation of the rod about the pin. NOTE: FOR PART A, IGNORE THE DAMPER. a) Determine the total kinetic energy of the system and the effective mass of the system with respect to 0. Use JG = 1 mr for the disk. b) Find the effective stiffness using the stiffness approach by setting 0 = 1. c) Let k = k = 1800 N/m, L = 1.2 m, m = 3 kg, c = 1.5 Ns/m. Determine: i) ii) iii) The effective damping of the system with respect to The damping ratio of the system Whether the system is underdamped, overdamped, or critically damped. K ww m L/3 L/3 ww Rod has no mass L/3 C