Nonlinear Piano-String Equations of Motion in State-Space Form

For the flexible (non-stiff) mass-spring string, referring to Fig.9.26 and Eq.(9.34), we have the following equations of motion:

or, in vector form,

Here the string terminations (bridge and agraffe) are modeled simply as very large masses and .

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.