Find the stiffness matrix (in local coordinates) for the two degree of freedom system displayed in Fig. P6.9. if \(k_{1}=2 \times 10^{5} \mathrm{~N} / \mathrm{m}, k_{2}=2 \times 10^{5} \mathrm{~N} / \mathrm{m}\), and \(k_{3}=1 \times 10^{5} \mathrm{~N} / \mathrm{m}\).

Fig. P6.9 Two degree of freedom system with a rigid, massless bar connecting the mass, \(m_{2}\), to a fixed pivot.

12 Pivot for rigid, massless bar k mi 1 m2 k2 X2