Nonlinear Spring Model
In the musical acoustics literature, the piano hammer is classically modeled as a nonlinear spring [493,63,178,76,60,486,164].10.14Specifically, the piano-hammer damping in Fig.9.22 is typically approximated by , and the spring is nonlinear and memoryless according to a simple power law:
The upward force applied to the string by the hammer is therefore
(10.20) |
This force is balanced at all times by the downward string force (string tension times slope difference), exactly as analyzed in §9.3.1 above.
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