The prepared doctoral dissertation focuses on studying dynamics of systems composed of magnetic pendulums subjected to a non-stationary magnetic field. A magnetic pendulum is a physical pendulum with a magnet attached to its end and is placed in an external magnetic field. The non-stationary external magnetic field is generated by an electric coil placed under the pendulum and powered by a time-varying current signal. The presented research mainly concerns the oscillations in one potential well of a single magnetic pendulum, as well as the control of the energy flow between two torsionally coupled magnetic pendulums.