A viscously damped single-degree-of-freedom system has a body of mass \(25 \mathrm{~kg}\) with a spring constant of \(70 \mathrm{kN} / \mathrm{m}\). Its base is subjected to harmonic vibration.

(a) When the base vibrates with an amplitude of \(50 \mathrm{~mm}\) at resonance, the steady-state amplitude of the body is found to be \(125 \mathrm{~mm}\). Find the damping ratio of the system.

(b) When the base vibrates at a frequency of \(10 \mathrm{~Hz}\), the steady-state amplitude of the body is found to be \(35 \mathrm{~mm}\). Find the magnitude of the force transmitted to the base.