  Internal friction effects are responsible for line widening of the resonance
frequencies in mechanical oscillators and result in damped oscillations of its
eigenmodes with a decay time Q/\omega. We study the solutions to the equations
of motion for the case of spherical oscillators, to be used as next generation
of acoustic gravitational wave detectors, based on various different
assumptions about the material's constituent equations. Quality factor
dependence on mode frequency is determined in each case, and a discussion of
its applicability to actual gravitational wave detectors is made on the basis
of available experimental evidence.
