Comparison of nonlinear oscillations of an electric monopole vs. a magnetic dipole

We consider two scenarios: First we drop an electric point-like charge with a chosen charge q in a nonuniform electrostatic field. We then seek for the criteria that in the presence of gravity the massive charge steadily oscillates. In the second scenario we drop a permanent magnet with a chosen magnetic dipole moment μ in a nonuniform magnetic field of a DC looping current. Similarly, we seek the criteria that in the presence of gravity the massive magnet steadily oscillates as well. In both cases the effective forces are nonlinear and the equations describing the motions are nonlinear analytically unsolvable differential equations. Utilizing Mathematica numeric scheme we solve these equations numerically. Plots of these solutions for selected parameters conducive to equal force couplings unveil the fundamental character differences of the oscillations. For comprehensive visual understanding we simulate the actual oscillations.