An air compressor of mass \(50 \mathrm{~kg}\) is mounted on an elastic support and operates at a speed of \(1000 \mathrm{rpm}\). It has an unbalanced mass of \(2 \mathrm{~kg}\) at a radial distance (eccentricity) of \(0.1 \mathrm{~m}\) from the axis of rotation. If the damping factor of the elastic support is \(\zeta=0.1\), determine the following:

(a) the spring constant of the elastic support which transmits no more than \(25 \%\) of the unbalanced force to the foundation, and

(b) the magnitude of the force transmitted to the foundation.