The equation should be
ξ ( t ) = c 1 ( [ 0 ω n 1 0 ω n 1 ] cos ω n 1 t + [ 1 0 1 0 ] sin ω n 1 t ) + c 2 ( [ 0 ω n 1 0 ω n 1 ] sin ω n 1 t − [ 1 0 1 0 ] cos ω n 1 t ) + c 3 ( [ 0 − ω n 2 0 ω n 2 ] cos ω n 2 t + [ − 1 0 1 0 ] sin ω n 2 t ) + c 4 ( [ 0 − ω n 1 0 ω n 2 ] sin ω n 2 t + [ 1 0 − 1 0 ] cos ω n 2 t ) . {\displaystyle \xi (t)=c_{1}\left({\begin{bmatrix}0\\\omega _{n_{1}}\\0\\\omega _{n_{1}}\end{bmatrix}}\cos \omega _{n_{1}}t+\left[{\begin{array}{c}1\\0\\1\\0\end{array}}\right]\sin \omega _{n_{1}}t\right)+c_{2}\left({\begin{bmatrix}0\\\omega _{n_{1}}\\0\\\omega _{n_{1}}\end{bmatrix}}\sin \omega _{n_{1}}t-{\begin{bmatrix}1\\0\\1\\0\end{bmatrix}}\!\cos \omega _{n_{1}}t\right)+c_{3}\left({\begin{bmatrix}0\\-\omega _{n_{2}}\\0\\\omega _{n_{2}}\end{bmatrix}}\!\cos \omega _{n_{2}}t+{\begin{bmatrix}-1\\0\\1\\0\end{bmatrix}}\!\sin \omega _{n_{2}}t\right)+c_{4}\left({\begin{bmatrix}0\\-\omega _{n_{1}}\\0\\\omega _{n_{2}}\end{bmatrix}}\!\sin \omega _{n_{2}}t+{\begin{bmatrix}1\\0\\-1\\0\end{bmatrix}}\!\cos \omega _{n_{2}}t\right).}
Return to errata.
![{\displaystyle \xi (t)=c_{1}\left({\begin{bmatrix}0\\\omega _{n_{1}}\\0\\\omega _{n_{1}}\end{bmatrix}}\cos \omega _{n_{1}}t+\left[{\begin{array}{c}1\\0\\1\\0\end{array}}\right]\sin \omega _{n_{1}}t\right)+c_{2}\left({\begin{bmatrix}0\\\omega _{n_{1}}\\0\\\omega _{n_{1}}\end{bmatrix}}\sin \omega _{n_{1}}t-{\begin{bmatrix}1\\0\\1\\0\end{bmatrix}}\!\cos \omega _{n_{1}}t\right)+c_{3}\left({\begin{bmatrix}0\\-\omega _{n_{2}}\\0\\\omega _{n_{2}}\end{bmatrix}}\!\cos \omega _{n_{2}}t+{\begin{bmatrix}-1\\0\\1\\0\end{bmatrix}}\!\sin \omega _{n_{2}}t\right)+c_{4}\left({\begin{bmatrix}0\\-\omega _{n_{1}}\\0\\\omega _{n_{2}}\end{bmatrix}}\!\sin \omega _{n_{2}}t+{\begin{bmatrix}1\\0\\-1\\0\end{bmatrix}}\!\cos \omega _{n_{2}}t\right).}](https://wikimedia.org/api/rest_v1/media/math/render/svg/aafb62d052eed9acd79ffd3192a8b8b2a2e37e14)
