Fig. 3. Mechanics of leg swinging as a function of frequency f, in terms of torque, work, and force/time, were modeled reasonably well by a forced pendulum (Equations 9, 10, 11). (a.) Hip torque amplitude, T₀, increased approximately with f² above natural frequency f_n (R²=0.96). (b.) Rate of mechanical work, ⁽⁺⁾, increased approximately with f³ (R²=0.93). (c.) Rate of force/time, , increased approximately with f ⁴ (R²=0.95). Metabolic cost is hypothesized to increase with both rate of work and force/time, for frequencies above the natural frequency f_n=0.64 Hz. Data fits were performed using dimensionless variables (right-hand axis) with body mass, gravitational constant, and leg length serving as base units; conventional units are shown (left-hand axis) for convenience. Data shown are mean ± S.D.