ASA 126th Meeting Denver 1993 October 4-8

3aMU1. The physics of normal modes.

Gabriel Weinreich

Randall Lab. of Phys., Univ. of Michigan, Ann Arbor, MI 48109-1120

This is primarily a tutorial paper to organize and clarify various concepts whose understanding is required for work with linear systems. Among the questions to be addressed are: What is the difference between a resonance and a normal mode? What about an antiresonance? How do normal modes relate to free motion? To forced motion? Are there ``strong'' and ``weak'' modes? Are resonance denominators quadratic in frequency, or linear? What does it mean for modes to be ``coupled''? In a measured frequency characteristic, when are normal modes represented by peaks, by dips, by both? What information is carried by the phase? In searching for normal modes, what is the difference between pulse excitation, white noise excitation, and sinusoidal excitation? Are there other options of interest? Do dissipative systems have normal modes? [Work supported by NSF.]