Introduction to Sports Biomechanics: Analysing Human Movement ...

INTRODUCTION TO SPORTS BIOMECHANICS
Figure 5.24 Transient response characteristics of a typical second-order force plate system 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). The output signal ‘settles’ to the input signal (the dashed black
horizontal line) far quicker for the critically damped case than for the other two.
208
To obtain a suitable transient response, the damping ratio needs to be around
0.5–0.8 to avoid under- or over-damping. A value of 0.707 is considered ideal, as in
Figure 5.24, as this ensures that the output follows the input signal – reaches steady
state – in the shortest possible time.
Careful inspection of Figure 5.23 allows the suitable frequency range to be
established for the steady-state response to achieve a nearly constant amplitude ratio
(Figure 5.23(a)) and a small phase lag (Figure 5.23(b)), with ζ = 0.707. The frequency
ratio ω′/ω n, where ω′ is the largest frequency of interest in the signal, must be small,
ideally less than 0.2. Above this value, the amplitude ratio (Figure 5.23(a)) starts to
deviate from a constant value and the phase lag increases and becomes very dependent
on the frequency, causing errors in the output signal. For impact forces, the natural
frequency should be 10 times the equivalent frequency of the impact, which can exceed
BOX 5.5 GUIDELINE VALUES FOR FORCE PLATE CHARACTERISTICS
Linearity ≤0.5% of full-scale deflection
Hysteresis ≤0.5% of full-scale deflection
Crosstalk ≤0.5% of full-scale deflection
Natural frequency ≥800 Hz
Maximum frequency ratio ≤0.2
(of signal frequency to natural frequency)
Damping ratio 0.5 to 0.8 (0.707 optimum)