Derive the general equations of motion, Equations 3.55 and 3.56 ,

\[ \begin{aligned} & m\left(\ddot{x}-\varepsilon \dot{\Omega}^{2} \cos \Omega-\varepsilon \ddot{\Omega} \sin \Omega\right)+k_{x} x=0 \\ & m\left(\ddot{y}-\varepsilon \dot{\Omega}^{2} \sin \Omega+\varepsilon \ddot{\Omega} \cos \Omega\right)+k_{y} y=0 \end{aligned} \]