Determination of dissipation force in oscillatory systems

The problem of estimating the dissipation force arising during the motion of a linear dissipative oscillator is considered. A method for determining the oscillator velocity and the viscous friction coefficient using only displacement measurements is proposed. It is based on the synthesis of invariant relations that allow us to relate the variables of a special extended dynamic system and determine the unknown variables as functions of the known ones. The efficiency of the proposed approach for the Duffing oscillator is demonstrated using numerical simulation.