§ DICTIONARY · CONCEPT
simple harmonic oscillator
System with a linear restoring force F = −kx; its solution is a pure sinusoid.
§ 01
Definition
A simple harmonic oscillator is any system whose equation of motion reduces to a mass times acceleration equal to minus a constant times displacement. The solution is a sine wave: position oscillates smoothly back and forth at a single frequency that depends only on the mass and the stiffness.
The simple harmonic oscillator is arguably the most important model in physics. Pendulums at small angles are SHOs. Springs are SHOs. LC circuits are SHOs. Atoms in a crystal lattice vibrate as SHOs. Every mode of every quantum field is an SHO. Whenever a stable equilibrium is gently disturbed, the first approximation is always a simple harmonic oscillator.