Feathering
Since the pluck model is linear, the parameters are not signal-dependent. As a result, when the string and spring separate, there is a discontinuous change in the reflection and transmission coefficients. In practice, it is useful to ``feather'' the switch-over from one model to the next [470]. In this instance, one appealing choice is to introduce a nonlinear spring, as is commonly used for piano-hammer models (see §9.3.2 for details).
Let the nonlinear spring model take the form









The foregoing suggests a nonlinear tapering of the damping in
addition to the tapering the stiffness
as the spring compression
approaches zero. One natural choice would be






In summary, the engagement and disengagement of the plucking system can be ``feathered'' by a nonlinear spring and damper in the plectrum model.
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Piano String Wave Equation
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Digitization of the Damped-Spring Plectrum