You will have to set up some equations, and then Mathematica can (numerically/analytically) solve them for you, and with the built in (List)ParametricPlot you will be able to plot those.
It just depends how much effort you want to put in to it. Within half an hour you should be able to make something that shows the trajectories of a system of masses.
Of course there is no built-in function that does exactly what you want, but with the wide variety of high-level functions it should be <20 lines of code I would estimate (depending on the complexity of course you look for of course).
To be honest, I would not know another piece of software that is as customisable as Mathematica and that is as easy as Mathematica. So Yes, go for Mathematica.
