The rotor of a dial indicator is connected to a torsional spring and a torsional viscous damper to form a single-degree-of-freedom torsional system. The scale is graduated in equal divisions, and the equilibrium position of the rotor corresponds to zero on the scale. When a torque of \(2 \times 10^{-3} \mathrm{~N}-\mathrm{m}\) is applied, the angular displacement of the rotor is found to be \(50^{\circ}\) with the pointer showing 80 divisions on the scale. When the rotor is released from this position, the pointer swings first to -20 divisions in one second and then to 5 divisions in another second. Find

(a) the mass moment of inertia of the rotor,

(b) the undamped natural time period of the rotor,

(c) the torsional damping constant, and

(d) the torsional spring stiffness.