An air compressor of mass 50 kg is mounted on elastic support and operates at a speed of 4 1000 rpm. It has an unbalanced mass of 2 kg at a radial distance (eccentricity) of 0.1 m from the axis of rotation. If the damping factor of the elastic support is ζ = 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.