Problem $(100$ points$)$: For the three$-$degree$-$of$-$freedom shear building in the figure. The lateral stiffness of floors $k_1=k_2=k_3=16357\mathrm{.}5{10}^{3}l\frac{b}{i}n.$ The floor mass $m_1=m_2=10000lb.s\frac{e{c}^2}{in}$ and $m_3=5000lb.s\frac{e{c}^2}{in}.$

Determine the natural frequencies and corresponding modal shapes.

Determine the normalized modal shapes of vibration.

Use MATLAB to verify the results.