\begin{array}{lcr}
(m_1 + 4m_3) \ddot{p} + 2m_3 \ddot{q} & = & (m_1 - 2m_3)g \\
2m_3 \ddot{p} + (m_2 + m_3) \ddot{q} & = & (m_2 - m_3)g
\end{array}