Escape dynamics of a forced-damped classical particle in an infinite-range potential well

The paper is devoted to analysis of the escape of periodically forced and damped particle from one-dimensional potential well. The particle is initially at rest, and the forcing is switched on at a certain time instance. The present work is an extension of previous results, obtained in Hamiltonian setting, for much more realistic case with viscous damping. Assuming primary 1:1 resonance, one can consider the problem in terms of averaged transient dynamics. It turns out that, similar to the undamped case, the escape process can be reliably described in terms of topology of special trajectories on the resonant manifold. A theoretical prediction to the minimal force required for the escape as function of the excitation frequency for various damping coefficients is provided. In the explored frequency range, numeric simulations are in complete qualitative and reasonable quantitative agreement with the theoretical predictions except for small frequencies under 0.3. These discrepancies are related to quasistatic asymptotic limit of the considered model.