Abstract: In the studies of both classical and quantum turbulence, significant attention is devoted to the investigation of the behavior of various submerged resonators. Upon entering the turbulent regime, the oscillators start to experience a significant drag force, which varies non-linearly with velocity. We present an empirical way of modeling such systems, and calculate the expected resonant response of such oscillators near the fundamental frequency as a function of the applied driving force. We apply the model to the crossover from linear to non-linear drag forces and compare with previous models as well as selected experimental data on the transition to turbulence in oscillatory flow of 4He.