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 weight of the engine and the floor is 2000 lb. At the rated speed of the engine, which is 600 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 k2 = 5000 lb/in.
(a) Find the weight of the mass to be attached to absorb the vibrations.
(b) What will be the natural frequencies of the system after the absorber is added?