The equations for the natural frequencies and mode shape vectors of a two degree-of-freedom system are

\[ \left[\begin{array}{cc} -\omega^{2}+3 & -2 \\ -2 & -\omega^{2}+2 \end{array}\right]\left[\begin{array}{l} 1 \\ \chi \end{array}\right]=\left[\begin{array}{l} 0 \\ 0 \end{array}\right] \]

(a) Define a system that would yield this equation.

(b) Calculate the natural frequencies of the system.

(c) Calculate the mode shape corresponding to the lower natural frequency.

(d) Draw a diagram illustrating the mode shape vector.