Two particles of masses $m_{1}$ and $m_{2}$ at positions $\mathbf{x}_{1}(t)$ and $\mathbf{x}_{2}(t)$ are subject to forces $\mathbf{F}_{1}=-\mathbf{F}_{2}=\mathbf{f}\left(\mathbf{x}_{1}-\mathbf{x}_{2}\right)$. Show that the centre of mass moves at a constant velocity. Obtain the equation of motion for the relative position of the particles. How does the reduced mass

$$\mu=\frac{m_{1} m_{2}}{m_{1}+m_{2}}$$

of the system enter?