Q$2$ The structural frame shown in Figure $2$ has a rigid and is rigidly jointed at both ends of the three columns. The mass of the structure of $5000kg$ is concentrated at the top. The columns are $3\mathrm{.}0m$ long and each has an $EI=4\mathrm{.}5106N-m^2.$ The structure has a viscous damping $()$ of $4\%.$ Model the structure as a SDOF shear building.

The top was displaced to the right by $25mm$ and then released. Compute the displacement, velocity and acceleration after one period. The plot the displacement as a function of time is shown $($Ordinate $5mm$ increments, Abscissa $0\mathrm{.}25sec$ increments$)$

$($a$)$ Calculate the undamped dynamic properties $($f$,$ T$,$ and $).($b$)$ Calculate the damped dynamic properties $,$ and $($c$)$ Using the plot in c$,$ determine the damping ratio $()$ using the log decrement method. Compare with the given damping ratio.

Figure $2$ Frame and Response