Approximate model for a viscoelastic oscillator

An oscillator where the restoring force is furnished by a viscoelastic bar and therefore depends on the history of the motion is considered. The history-dependent force is characterized by a relaxation modulus and a relaxation time. Assuming that the relaxation time is small, an approximate model for the oscillator is derived. This model is then linearized for the study of small vibrations. It is shown that the viscoelastic force, in addition to viscous damping, effects an apparent decrease in mass that modifies the natural frequency of the linear oscillator. The temperature dependence of the relaxation time, and consequently the frequency shift, is studied.