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The focus is the power formulae relating periodic time in terrestrial locomotion and flight to mass and length. The periodic timing of limbs and wings oscillating comfortably in absolute co-ordination is viewed as the characteristic period τ₀ of a system in which the free, undamped oscillatory motion of a point mass m at a distance l from a fixed axis does work against two conservative forces. These forces are in the form of gravity g acting on the point mass and a spring of stiffness k acting at a distance b from the axis. The system's characteristic period can be expressed most simply as: τ₀ = 2π[ml²/(mlg + kb²)]^1/2. In the biological instantiation of this hybrid mass-spring/simple pendulum system, muscular and other tissues function as the spring that elastically stores and releases mechanical energy. Regular oscillations are brought about and sustained by a muscular driving force that ordinarily is close to resonance. The …