# Passage through resonance for a system with time-varying parameters possessing a single trapped mode

@article{Shishkina2019PassageTR, title={Passage through resonance for a system with time-varying parameters possessing a single trapped mode}, author={Ekaterina V. Shishkina and S. N. Gavrilov and Yulia A. Mochalova}, journal={arXiv: Classical Physics}, year={2019} }

We consider a forced oscillations of an infinite-length mechanical system, with time-varying parameters, possessing a single trapped mode characterized by frequency $\Omega_0(\epsilon t)$. The system is a string, lying on the Winkler foundation, and equipped with a discrete linear mass-spring oscillator of time-varying stiffness. The discrete oscillator is subjected to harmonic external force with constant frequency $\hat\Omega$. In the case of the passage through the resonance, we obtain the…

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