Free Vibration and Hysteretic Damping

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Abstract
If the definition that hysteretic damping is proportional to displacement but in phase with velocity be accepted, then the free vibration of a simple oscillator may be treated, without ambiguity, using this concept. The apparent anomaly which Dr. Bishop points out in his paper “ The Treatment of Damping Forces in Vibration Theory ” (November 1955 Journal) arises through confusing three distinct possible mathematical representations of some unspecified vibrating system.

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