Natural oscillations in a log-periodic chain of oscillators

An analysis is presented of natural oscillations in a log-periodic chain (LPC) of oscillators; the simple case of a chain of coupled oscillators is considered, though the proposed formalism can be extended to more complex LPCs. It is shown that natural oscillations in an LPC of oscillators can be fully described if the base frequency and the corresponding eigenvector are known. The governing equations are obtained, and the explicit form of the eigenvector is determined for the case of weak coupling between the oscillators.