The friction force in many physical systems has been found to depend on a power of the velocity, the magnitude of which varies according to the damping mechanism. This note employs an approximate theory applicable to small damping to examine the free vibration of a single degree of freedom system in which the damping force is proportional to an unspecified power of the velocity.

Correlation with experimental data on the internal damping of solid materials shows that this phenomenon also tends to obey a power law although discrepancies exist between the expected and observed behaviours. These arise from the interpretation of the damping coefficient and from the frequency dependence of the dissipated energy.