Problem $3)$ The normal mode of a three storey shear building with identical mass $($m$)$ in each storey and lateral storey stiffress $(k)$ are given by

$\{{\}}^{(1)}=\{[0\mathrm{.}737],[0\mathrm{.}591],[0\mathrm{.}328]\}$;$\{{\}}^{(2)}=\{[-0\mathrm{.}591],[0\mathrm{.}328],[0\mathrm{.}737]\}$;$\{{\}}^{(3)}=\{[0\mathrm{.}328],[-0\mathrm{.}737],[0\mathrm{.}591]\}$

Verify the orthogonality properties using modal matrix. Further, the system is given an initial displacement of

$\{u(0)\}=\{[0\mathrm{.}520],[-0\mathrm{.}10],[0\mathrm{.}205]\}$

and released. Determine the free vibration response and contribution of each mode in governing the free vibration responses.