A particle of mass $m_{1}$ is constrained to move on a circle of radius $r_{1}$, centre $x=y=0$ in a horizontal plane $z=0$. A second particle of mass $m_{2}$ moves on a circle of radius $r_{2}$, centre $x=y=0$ in a horizontal plane $z=c$. The two particles are connected by a spring whose potential energy is

$$V=\frac{1}{2} \omega^{2} d^{2}$$

where $d$ is the distance between the particles. How many degrees of freedom are there? Identify suitable generalized coordinates and write down the Lagrangian of the system in terms of them.