Q$2$: $[$Forced damped vibration$]$

A $400-$ kg motor supported by four springs, each of constant $\backslash (150\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}\backslash ),$ and a dashpot of constant $\backslash (\backslash$mathrm$\{$c$\}=\backslash )\backslash (6500\backslash$mathrm$\{$~N$\}\backslash$cdot $\backslash$mathrm$\{$~s$\}/\backslash$mathrm$\{$m$\}\backslash )$ is constrained to move vertically. Knowing that the unbalance of the rotor is equivalent to a $23-$g mass located at a distance of $100$ mm from the axis of rotation, determine for a speed of $800$ rpm$,$ the amplitude of the vertical motion of the motor.