An elementary model consisting of one charged particle in a viscous medium exposed to weak ac-dc low-frequency magnetic fields is analyzed to identify and explain the fundamental characteristics of the physical mechanisms that result in a resonance response, which is similar to the familiar cyclotron resonance. The model predicts both frequency and amplitude windows, which are explained in terms of synchronization of the particle with electric fields. Although extrapolation of model results to biological systems is limited by the elementary nature of the model, the model results indicate that observed resonant responses by others of biological systems to ac-dc magnetic fields are probably not due to resonant response of ions in solution, since the model predicts that no resonant response is possible unless the viscous damping is very low, many orders of magnitude lower than the viscous damping of ions in solution.