The equations of motions for a Foucault pendulum are given by:
$$\ddot{x} = 2\omega \sin\lambda \dot{y} - \frac{g}{L}x,$$ $$\ddot{y} = -2\omega \sin\lambda \dot{x} - \frac{g}{L}y.$$
What are the equations describing $\dot{x}$ and $\dot{y}$?
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