Problem $2$: The structure below is an undamped two$-$story shear building structure. You may

assume that the mass $(m)$ is $0\mathrm{.}3$kips$-i\frac{n}{s^2}$ and the stiffness $(k)$ is $170\frac{k}{i}n.$ Use of MATLAB or

other software allowed to conduct the eigenvalue analysis.

$($a$)(10$ points$)$ Determine the equations of motion for the structure above assuming the

beams are rigid in flexure and axial deformations are neglected.

$($b$)(10$ points$)$ Determine the natural vibration frequencies and modes.

$($c$)$ points$)$ Normalize the modes with a unit displacement at the roof.