$2.$ A machine weighing $2000$ N rests on a support. The support deflects $5$ cm as a result of the weight of the machine. The floor under the support is somewhat flexible and moves because of the motion of a nearby machine, harmonically at resonance with an amplitude of $0\mathrm{.}2$ cm $.$ Model the floor as a moving base and assume a damping ratio $\backslash (\backslash$zeta$=0\mathrm{.}01\backslash ).$ Calculate

$($a$)$ the amplitude of the displacement at resonance

$($b$)$ the amplitude of the displacement at $0\mathrm{.}75$ times the resonant frequency.

$\backslash [$

A$=0\mathrm{.}2\backslash$mathrm$\{$~cm$\}$

$\backslash ]$