The plucked string: an example of non-normal dynamics
arXiv:1406.6939 · doi:10.1119/1.4902310
Abstract
Motion of a single Fourier mode of the plucked string is an example of transient, free decay of coupled, damped oscillators. It shares the rarely discussed features of the generic case, e.g., possessing a complete set of non-orthogonal eigenvectors and no normal modes, but it can be analyzed and solved analytically by hand in an approximation that is appropriate to musical instruments' plucked strings.
18 pages, 3 figures; revised to include reference to additional examples of transient growth and non-normal dynamics and expanded to include the most general coupling of vertical to horizontal string modes and not just the simplest example presented earlier