Dynamics | Part IA, 2001

Two particles of masses m1m_{1} and m2m_{2} at positions x1(t)\mathbf{x}_{1}(t) and x2(t)\mathbf{x}_{2}(t) are subject to forces F1=F2=f(x1x2)\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

μ=m1m2m1+m2\mu=\frac{m_{1} m_{2}}{m_{1}+m_{2}}

of the system enter?

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