  The paper addresses an escape of a classical particle from a potential well
under harmonic forcing. Most dangerous/efficient escape dynamics reveals itself
in conditions of 1:1 resonance and can be described in the framework of
isolated resonant (IR) approximation. The latter requires reformulation of the
problem in terms of action-angle (AA) variables, available only for a handful
of the model potentials. The paper suggests approximation of realistic generic
potentials by low-order polynomial functions, admissible for the AA
transformation, with possible truncation. To illustrate the idea, we first
formulate the AA transformation and solve the escape problem in the IR
approximation for a generic quartic potential. Then, the model problem for
dynamic pull-in in microelectromechanical system (MEMS) is analyzed. The model
electrostatic potential is approximated by the quartic polynomials (globally
and locally), and quality of predicting the escape thresholds is assessed
numerically. Most accurate predictions are delivered by global $L^2$-optimal
heuristic approximation.
