Introduction to Sports Biomechanics: Analysing Human Movement ...

CAUSES OF MOVEMENT – FORCES AND TORQUES
A force plate is a measuring system consisting essentially of a mass (m), a spring of
stiffness k, and a damping element (c), rather like a racing car’s suspension system; some
simple models of the human lower extremity also use such a mass–spring–damper
model. The ‘steady-state’ frequency response characteristics of such a system are usually
represented by the unique series of non-dimensional curves of Figure 5.23. The
response of such a system to an instantaneous change of the input force is known as its
‘transient’ response and can be represented as in Figure 5.24.
In these two figures:
The ‘damping ratio’ of the system, ζ = c/√(4 k m)
The ‘frequency ratio’ (ω/ω n) is the ratio of the signal frequency (ω) to the ‘natural
frequency (ω n)’ of the force plate
The natural frequency ω n = √(k/m), is the frequency at which the force plate will
vibrate if struck and then allowed to vibrate freely.
Figure 5.23 Steady-state frequency response characteristics of a typical second-order force plate system: (a) amplitude plot;
(b) phase plot for damping ratios of: 2 (overdamped case shown by the dashed blue curve), 0.707 (critically damped case
shown by the continuous black curve), and 0.2 (underdamped case shown by the continuous blue curve).
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