SOLVE $$T BY GIVING YOUR VALUES $.$Q$3.$ The steel frame shown in Fig. is fixed at its base and has a rigid top that weighs $2000$kn a$)(20$P$)$ Write the equation of motion of the following undamped SDOF system for free vibration. If the initial displacement is $10$ and the initial velocity is $15,$what is the displacement at t$=3$sec $?$ b$)(20$P$)$ If the frame supports a rotating machine, which exerts a horizontal force at the girder level of P$($t$)=$P$\_(0)$sin$(\backslash$omega t$),$ determine the steady$-$state amplitude of vibration. Consider a damping ratio of $\backslash$xi $\%$ for the system. Also, $\backslash$omega $=0\mathrm{.}25\backslash$omega $\_($n$).$