"Warning: I'm still not sure what the right answer is. [...but...]
Atomic nuclei are pulled together by the electrostatic
attraction between negatively-charged electron clouds and
positively-charged nuclei.
Atomic nuclei are kept apart by Schrödinger pressure.
When the nuclei get too close, their electron clouds get
crowded, and as they don't like to overlap, they push the
nuclei back."
Since everything
on the web is true. That explaination is good enough for me! This
explaination describes oscillatory motion for atomic bonds. According
to a physics major that I talked to, the oscillatory motion of atoms is
not exactly sinusoidal (that of a spring), but can be approximated by
it in a hand-waving fasion.
Simulated atoms:
My physics book, "Physics for scientists and
engineers," states: "The forces between atoms in a solid can be modeled
by imagining springs between neighboring atoms." This goes along with
what my physics major freind said about atomic bonds, and gives me full
mandate to begin programming my matter-physics simulation using spring
bonds to describe matter!