Using the statically condensed stiffness matrix shown below $($corresponding to $1^{st}$ and $2^{nd}$ degrees of freedom, respectively$)$:

$1-$ Develop the Modal Stiffness $($K$),$ and Modal Mass $($M$)$ for the structure shown below.

$2-$ Use a modal damping ratio of $2\%$ in the first mode and $3\%$ in the second mode to analyze the structure for the horizontal Heathcote Valley record from the Christchurch earthquake $($See the record in the attached Excel Sheet$)$ using Modal Response History Analysis. You can use the Newmark or any other method to solve the SDOF modal equations. Plot the modal displacements and total displacement time histories for the $1$ st and $2$ nd degrees of freedom.

$k$:$=([-79\mathrm{.}8,55\mathrm{.}6])\frac{1}{in}$