ABSTRACT
The computational expense could be worth it, if the masses and springs all have different coefficient values (this is called an inhomogeneous medium), or, if we need lots of spatial resolution for a simulation. Imposing arbitrary boundary conditions (such as a strange boundary shape like a small star or jagged edge of broken glass, for instance) might require a high spatial resolution. Note that we might not need all the resolution for the final sound output, because of the natural bandwidth limitation of our hearing. But remember that our simple one mode mass/spring/damper system had to be calculated at higher than the audio rate in order to behave realistically. So we might expect that the spatial resolution of a two-or higher-dimensional simulation might need to be quite high to make the system behave correctly, and to make the actual computations stable and realistic.
