A 50-kg machine tool is mounted on an elastic foundation. An experiment is run to determine the stiffness and damping properties of the foundation. When the tool is excited with a harmonic force of magnitude \(8000 \mathrm{~N}\) at a variety of frequencies, the maximum steady-state amplitude obtained is \(2.5 \mathrm{~mm}\), occurring at a frequency of \(32 \mathrm{~Hz}\). Use this information to determine the stiffness and damping ratio of the foundation.