$3.$ A car runs on a multi$-$span bridge whose surface can be expressed as a sine wave with amplitude of $7\mathrm{.}5$ cm $,$ and the length of each span is $30$ m $.$ The car can be simplified as a SDOF whose mass $\backslash (=1\mathrm{.}8\backslash$mathrm$\{$t$\}\backslash ),$ equivalent stiffness $\backslash (\backslash$mathrm$\{$K$\}=140\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}\backslash ),$ and the equivalent damping ratio $\backslash (=40\backslash \%\backslash )$

Q$1$: if speed of the car is $\backslash (80\backslash$mathrm$\{$~km$\}/\backslash$mathrm$\{$h$\}\backslash ),$ the vertical displacement

Q$2$: Determine the speed for resonance vibration