| Spring motion is the motion of systems where the force is proportional to the distance. Many interesting systems (like springs) are near equilibrium, which means that the potential energy is at a local minimum. A spring is an example, but also a pendulum. When the potential is at a local minimum, its gradient is zero. So if you Taylor expand it you only get second-order contributions. For a spring, the potential energy looks like V(x) = V(0) + k * x * 2 where x is the displacement and k is a constant. Differentiating, you get harmonic motion: F(x) = k * x Broadly speaking, this applies to all systems near equilibrium, simply from Taylor expanding the energy. And it's not only in classical mechanics, but in all branches of physics. Sydney Coleman [0] is often quoted as saying something like "QFT is simple harmonic motion taken to increasing levels of abstraction." [1] [0] https://en.wikipedia.org/wiki/Sidney_Coleman [1] https://physics.stackexchange.com/questions/355487/qft-is-si... |