Why isn't motility most efficient at pendulum frequency?

3 reasons:

  1. The power dissipated by a damped resonant system is not minimum, but maximum, at resonance:
        


  2. Animal locomotion is certainly not resonant! —more like an inverted pendulum:


  3. Empirically the frequencies don't agree with the calculated (inverted) pendulum ones:

    Predicted and observed
    stepping frequencies
    for l = 1 m
    Predicted | Observed
    Walk:   0.6 Hz   0.85–0.9 Hz
    Run:   1.13 Hz   1.65–2.0 Hz