$($a$)$ A two$-$story building is modelled as a $2-$DOF system and the structural system can be modelled as a shear beam building. The second floor has $\frac{2}{3}$ of the first$-$floor stiffness and mass.

$k=400\frac{N}{m}$ and the floor mass, $m=10000kg.$ Determine the eigenvalue and eigenvectors of all modes.