Suppose the system of Equation 6.38, [ begin{aligned} & {left[begin{array}{cc} m_{1} & 0 0 & m_{2} end{array} ight]left{begin{array}{l} ddot{x}_{1} ddot{x}_{2} end{array} ight}}

Suppose the system of Equation 6.38,

\[ \begin{aligned} & {\left[\begin{array}{cc} m_{1} & 0 \\ 0 & m_{2} \end{array}\right]\left\{\begin{array}{l} \ddot{x}_{1} \\ \ddot{x}_{2} \end{array}\right\}} \\ & +\left[\begin{array}{cc} k_{11} & k_{12} \\ k_{21} & k_{22} \end{array}\right]\left\{\begin{array}{l} x_{1} \\ x_{2} \end{array}\right\}=\left\{\begin{array}{l} F_{1}(t) \\ F_{2}(t) \end{array}\right\} \end{aligned} \]

is forced by the vector \(\left\{F_{1}(t) \quad F_{2}(t)\right\}^{T}=\) \(\left\{f_{1} \cos \omega_{1} t \quad f_{2} \cos \omega_{2} t\right\}^{T}\). Solve for the general response using the direct method.

m1 0 X1 k11 k12 X 0 m2 X2 k12 K22 X2 f1 (6.39) 0