An electric motor running at \(450 \mathrm{rpm}\) is supported on a spring and a dashpot. The spring stiffness is \(6000 \mathrm{~N} / \mathrm{m}\) and the dashpot offers resistance of \(500 \mathrm{~N}\) at \(5 \mathrm{~m} / \mathrm{s}\). The unbalanced mass \(0.5 \mathrm{~kg}\) rotates at \(6 \mathrm{~cm}\) radius and the total mass of vibratory system is \(20 \mathrm{~kg}\). Determine

(a) damping factor,

(b) amplitude of vibration and phase angle,

(c) resonant speed and resonant amplitude, and

(d) force exerted by the spring and dashpot on the motor.