Noise-induced transitions between coexisting stable states of a periodically driven nonlinear oscillator have been investigated by means of analog experiments and numerical simulations in the nonadiabatic limit for a wide range of oscillator parameters. It is shown that, for over-damped motion, the field-induced corrections to the activation energy can be described quantitatively in terms of the logarithmic susceptibility (LS) and that the measured frequency dispersion of the corresponding corrections for a weakly damped nonlinear oscillator is in qualitative agreement with the theoretical prediction. Resonantly directed diffusion is observed in numerical simulations of a weakly damped oscillator. The possibility of extending the LS approach to encompass escape from the basin of attraction of a quasi-attractor is discussed.