Identifying a differential equation for lip motion

A second order homogeneous differential equation is fitted to lip trajectories during speech at fast, normal, and slow speaking rates. The objective is to characterize lip motion in terms of biomechanical parameters such as stiffness, damping, and applied external forces. The results show that, at fast speaking rates, the lip behaves like a simple mass-spring oscillator moving at its natural frequency, and with low variability across repetitions. At slow speaking rates, on the other hand, the lip is under a stronger external control to conform to the required trajectory, which introduces a larger variability accross repetitions. The case of normal rate falls between the fast and slow rate cases.