<p>The problem of finding the coefficients of a Fourier series that approximates a periodic force acting on a nonlinear oscillator has been considered. A method has been proposed to solve the corresponding problem of real-time estimation of the oscillator velocity and the coefficients of the partial sum of the Fourier series by means of only displacement measurements. This method is based on the synthesis of invariant relations that make it possible to interrelate the variables of a special extended dynamic system and determine unknown variables as functions of known ones. The asymptotic convergence of the estimates of unknowns to their true values has been proven. The efficiency of the proposed approach for the Duffing oscillator has been demonstrated through numerical simulation.</p>