$$ \begin{pmatrix} 0 \\ 0 \end{pmatrix} = \begin{pmatrix} \frac{k+K}{m}-\lambda^2 & \frac{-K}{m} \\ \frac{-K}{m} & \frac{k+K}{m}-\lambda^2 \end{pmatrix} \begin{pmatrix} v_1 \\ v_2 \end{pmatrix}$$