Problem You will be processing the experimental data from the forced response tests of the single$-$story building model. The experimental data is available on Canvas. As a group, you must upload to Canvas a PDF document with the following items:

$1.$ Assuming the system parameters identified from the free response tests $\backslash (\backslash$left$($f$\_\{$n$\}=6\mathrm{.}135\backslash$mathrm$\{$~Hz$\}\backslash$right$.\backslash )$ and $\backslash (\backslash$zeta$=\backslash )0\mathrm{.}0053),$ plot the ground acceleration and total acceleration time histories for a forcing frequency $\backslash ($ f$=4\mathrm{.}5\backslash$mathrm$\{$~Hz$\}\backslash )$ and a ground$-$motion amplitude of $\backslash (\backslash$ddot$\{$u$\}\_\{$g o$\}=0\mathrm{.}1\backslash$mathrm$\{$~g$\}\backslash ).$

$2.$ Plot the experimentally measured transmissibility TR versus the forcing frequency $\backslash ($ f $\backslash ).$ On the same axes plot the theoretical TR versus forcing frequency assuming the natural frequency and damping ratio determined from the free response tests.

$3.$ Calculate the square$-$root sum$-$of$-$squares $($SRSS$)$ error between the measured TR and the predicted TR with the values from the free response tests.

$4.$ Assuming the natural frequency determined from the free response tests $(\backslash ($ f$\_\{$n$\}=6\mathrm{.}135\backslash$mathrm$\{$~Hz$\}\backslash )),$ tune the damping ratio to minimize the SRSS error between the measured TR and the predicted TR$.$ Report the optimal fitted $\backslash (\backslash$zeta $\backslash )$ and the corresponding SRSS error, and plot the predicted TR versus forcing frequency assuming the fitted $\backslash (\backslash$zeta $\backslash )$ value on the same axes as the experimentally measured TR$.$