natural frequency

The frequency at which a system oscillates _on its own_, with no external driving and no damping. For a mass-spring system: `ω₀ = √(k/m)`. For a small-angle pendulum: `ω₀ = √(g/L)`. For an electrical LC circuit: `ω₀ = 1/√(LC)`. Different physics, same shape — `ω₀² = stiffness / inertia`. Damping shifts the apparent frequency slightly downward; driving forces _don't_ change `ω₀` but cause large response when their frequency comes close to it (_resonance_). Every system has at least one natural frequency; complex systems (a bridge, a guitar string, a building) have many.