Find the stiffness matrix (in local coordinates) for the two degree of freedom system displayed in Fig. P6.7. 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. P6.7 Two degree of freedom system with a rigid, massless bar connecting the two masses, \(m_{1}\) and \(m_{2}\)

x1 mi k 12 kz. 2 X2 m2 k2 (2