In Physics we see that $\vec{F}=\frac{\mathrm{d}\vec{p}}{\mathrm{d}t}$ where $\vec{p}=m\vec{v}$ but here we say the external forces (which is in kg m/s^2, per F=ma) is found by adding momentum (which is in kg m/s). How do these units match up — especially since on the previous slide the Professor warned us to be careful about units

Also why does the error get smaller when we make the masses smaller (approaching point masses)?

I think errors get smaller for smaller masses because they become more similar to an ideal point mass, which are more accurately represented by our simplified model of physics.

This equation is the same as we're learning in Systems and Signaling to translate between frequency responses. I'm curious if these signals will relate and convert to the Fourier transform to take out each point of the mesh and determine its specific movements in some way. It might help in combining and separating the movements from the different springs.

@mylinhvu11, of course you can. Fourier transform can be applied on any systems with similar mathematical form. In fact, since the good quality of $e^x$, it should be a powerful tool when solving any differential equation.