A torsional pendulum as in Figure above has a natural frequency of 200 cycle/min when vibrating in vacuum. The mass moment of inertia of the disk is 0.2 kg-m. It is then immersed in a viscous fluid which produces a damping constant of c, to the system. The natural frequency of the system is found to have changed to 180 cycle/min. Discuss the changes of the system's frequency (in rad/s) which is caused by the oil and identify the damping constant of the system. The disk is given an initial displacement 0,= 2 when it is placed in the fluid. Identify displacement of the disk at the end of the first cycle where t = td- (b) Fluid, c, Shaft, k Disc, Jo