The nonlinear forced vibrations of two pendulums coupled by an elastic element are considered. One of the pendulums is subjected to the magnetic stimulus produced by a pair of a periodically powered coil and a permanent magnet mounted at the end of the pendulum. We extend our previous experimental and numerical results presented in Polczyński et al. (2019) and proposed a new rational approximation of a magnetic torque to enable the application of analytical methods. Based on this approximation, the numerical and analytical studies of equations of motion are carried out. In particular, the resonant phenomena and periodic regimes are studied in detail. The procedure to approximate the subharmonic and almost harmonic regimes is developed using the balance harmonic method. The successive maxima map has been employed to study more complicated regimes. This technique allows one to reveal changes in profile’s shapes for various driving frequencies and shows the existence of strongly chaotic trajectories.

考虑由弹性元件耦合的两个摆的非线性强迫振动。一个钟摆受到一对周期性供电的线圈和一个安装在钟摆末端的永磁体产生的磁刺激。我们扩展了先前在Polczyński等人中提出的实验和数值结果。（2019）并提出了一种新的磁转矩有理近似值，以使分析方法得以应用。基于此近似值，对运动方程进行了数值和分析研究。特别是，对共振现象和周期状态进行了详细研究。使用平衡谐波法开发了近似于次谐波和几乎谐波状态的程序。连续的最大值图已经被用来研究更复杂的情况。