A reciprocating engine is installed on the first floor of a building, which can be modeled as a rigid rectangular plate resting on four elastic columns. The equivalent mass of the engine and the floor is \(1000 \mathrm{~kg}\). At the rated speed of the engine, which is \(600 \mathrm{rpm}\), the operators experience large vibration of the floor. It has been decided to reduce these vibrations by suspending a spring-mass system from the bottom surface of the floor. Assume that the spring stiffness is \(k_{2}=875 \mathrm{kN} / \mathrm{m}\).

(a) Find the mass to be attached to absorb the vibrations.

(b) What will be the natural frequencies of the system after the absorber is added?