A machine supported symmetrically on four springs has a total mass of 100 kg. It has unbalance reciprocating parts of 2.0 kg which moves through a vertical stroke of 100 mm with simple harmonic motion. The machine is having only one degree of freedom and can undergo vertical displacement. Evaluate its natural frequency and combined stiffness of the springs if the force transmitted to the foundation is one-twentieth of the applied force, when there is no damping in the system. The machine is rotating at 800 rpm. When the machine is actually tested for vibration, it is found that the damping present in the system reduces the amplitude of successive free vibrations by 30%. Evaluate:
(i) the actual force transmitted to foundation at the running speed 800 rpm.
(ii) the force transmitted in foundation at resonance, and
(iii) the amplitude of vibration of the machine due to unbalance mass, at resonance.