In this Letter, we propose a simple method to recover the unknown parameters and the velocity state from a known suitable output which is the position of the Duffing mechanical oscillator. We show that the system is constructible. Hence, it allows us to obtain an integral output parametrization of the remaining state. Based on this integral parametrization, we construct an iterative integral equation of the output. This method is numerically feasible and easy to implement by means of integrators, avoiding the necessity to evaluate the derivatives of the output.