Vibrations of a moving threadline

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Abstract

The characterization and analysis of the oscillation of a string as it is traversed and wound on a bobbin are considered. A mathematical model is formulated and solved for the oscillations of an infinite and finite threadline between a fixed eyelet and the traverse device. The methods of D'Alembert and of characteristics are applied and the importance of the ratio of the winding speed to the string's characteristic wave velocity is demonstrated.

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