A machine is mounted on an elastic support with negligible damping. The machine has an

unbalanced rotor. It was noticed that the maximum amplitude of vertical vibration occurs

when the unbalanced rotor is rotating at $1600rpm.$ In order to determine the mass of the

machine and the stiffness of the support, a spring$-$mass system, of mass $3kg,$ tuned to $1600$

cpm$,$ was attached to the machine to act as a tuned vibration absorber$.$ With this arrangement,

resonance occurred at rotor speeds $1505rpm$ and $1701rpm,$ and the steady state amplitude

of the absorber mass was $2mm$ when the rotor was rotating at $1600rpm.$ Determine the mass

of the machine and the stiffness of the support.

A vibration absorber$,$ tuned to $1600cpm,$ is to be used to provide a speed range $384rpm$

between the resonance speeds. Determine:

a$)$ The mass and stiffness of this absorber$.$

b$)$ The amplitude of the mass of this absorber during its steady state operation, when the

unbalanced rotor is rotating at $1600rpm.$