restoring force

A restoring force is any force that tries to push a system back to its resting state, and whose strength grows with how far the system has been displaced. The simplest form is F = −kx, where x is the displacement and k is a stiffness constant. The minus sign is the whole point: the force always points back toward zero.

This is the mathematical seed of every oscillator in physics. Pendulums, springs, plucked strings, vibrating atoms in a crystal, LC circuits, the modes of a quantum field — all of them share the same equation, with only the constants changing.