Comment by ndriscoll

F=ma is slightly important for physics, no? And deriving the equations is kind of the point; it's the understanding of "why" something is true.

e.g. I can tell you things act like a spring near (stable) equilibrium, and you can believe me, but why on Earth would that be true? Well, Taylor expand the potential at equilibrium. Define V(0)=0, and equilibrium means V'(0)=0, so V(x) ~ V''(0)/2 x^2, so F = -dV/dx = -V''(0)x, which is a spring with spring constant k=V''(0).

That's all a very conceptual explanation; the point is near an equilibrium, zoom in and you have a parabolic potential! What is the potential for a spring? A parabola! This is basic Calc BC stuff, but it also justifies why we might care about about simple harmonic motion. Calculus is the whole business of "zooming in."