From AMS Glossary
(Also called characteristic frequency.) Any frequency of small-amplitude oscillation for a system with a position of stable equilibrium and in the absence of external forces.
One must be careful about what is meant by "external forces." A simple pendulum of length h, when disturbed slightly from its equilibrium position, oscillates with natural (circular) frequency
where g is the acceleration due to gravity. Yet this oscillation requires an external force, namely, gravity. In general, a mechanical system with a position of stable equilibrium has a set of distinct natural frequencies, one for each degree of freedom.