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\begin{document}
\begin{equation*}
  \begin{aligned}
    \frac{dx}{dt} &= \begin{bmatrix}
      0 & 1 & 0 & 0 \\ -k/(m_1+m_2) & -c/(m_1+m_2) & 1/m_2 & 0 \\ 
      0 & 0 & 0 & \omega_3 \\ 
      0 & 0 & -\omega_3 & -2 \zeta_3 \omega_3
    \end{bmatrix} x + \begin{bmatrix}
      0 \\ 0 \\ 0 \\
      \omega_3^2
    \end{bmatrix}u, \\    
    y &= \frac{m_2}{m_1+m_2}\begin{bmatrix}\dfrac{m_1k}{m_1+m_2}&
      \dfrac{m_1c}{m_1+m_2}& 1& 0 \end{bmatrix}x.
  \end{aligned}
\end{equation*}
\end{document}