The half-width and separation of the components of a close high-Q doublet and the normal modes of vibration of circular rings with rectangular cross-sections

With axially symmetrical vibrating systems like rings, cones and bells most of the normal modes occur as degenerate doublets with the two components having equal Q values. If a slight asymmetry is introduced into the system - either structural or metallurgical - these doublets split slightly and often interest centres on the amount of this splitting. The easiest method to measure this is both to drive and detect at one point midway between the two nodal/antinodal meridians of the two components. By driving the system at this "symmetry" radian frequency of the doublet response a beating decay is observed if the drive is switched off after attaining the steady state. [Continues.]