Following the methodology of this section, study a forced vibrating system with the following property matrices,

\[[m]=\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right], \quad[k]=\left[\begin{array}{cc} 2 & -1 \\ -1 & 1 \end{array}\right]\]

where each component force vector \(\left\{F_{1}(t) F_{2}(t)\right\}^{T}\) is white noise. Transform the coupled equations of motion into modal coordinates and proceed with an analysis of this two degree-of-freedom system. Discuss any assumptions needed in progressing through the steps of the analysis.