#### 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