A torsional pendulum has a natural frequency of \(200 \mathrm{cycles} / \mathrm{min}\) when vibrating in a vacuum. The mass moment of inertia of the disc is \(0.2 \mathrm{~kg}-\mathrm{m}^{2}\). It is then immersed in oil and its natural frequency is found to be 180 cycles/min. Determine the damping constant. If the disc, when placed in oil, is given an initial displacement of \(2^{\circ}\), find its displacement at the end of the first cycle.