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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.doi:10.1119/1.4902310 fatcat:e4xur7bb7nfetaacehwmcfwhca