$w_1=\sqrt[\phantom{2}]{\frac{k}{2m}}\{a{\}}_1=\{[\frac{1}{2}],[1]\},w_2=\sqrt[\phantom{2}]{\frac{2k}{m}},\{a{\}}_2=\{[-1],[1]\}$

Determine $\{[u_1],[u_2]\}$ under the applied dynamic loading.

$=>[A]=\left[\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right]=\left[\begin{array}{cc}\frac{1}{2}& -1\\ 1& 1\end{array}\right],\{p\}=\{[p_{0}sinwt],[0]\}$