A new perspective on the ubiquity of classical harmonic oscillators is presented based on the two-variable Taylor expansion of a perturbed system's total energyE(q,q̇), whereq(t) is the system displacement as a function of timetandq̇(t)=dq/dt. This generalised approach permits derivation of the lossless oscillator equation from energy arguments only, yielding a universal equation for the oscillation frequencyω=(∂2E/∂q2)/(∂2E/∂q̇2)which may be applied to arbitrary systems without the need to form system-specific linearised models. As illustrated by a range of examples, this perspective gives a unifying explanation for the prevalence of harmonic oscillators in classical physics, can be extended to include damping effects and driving forces, and is a powerful tool for simplifying the analyses of perturbed systems.