Experimental Study of Kramers' Rate in a Magnetically Driven Duffing Oscillator

A Duffing oscillator is a damped, periodically driven, and bistable system which does not perfectly obey Hooke’s Law and can therefore be described as nonlinear. This nonlinearity produces interesting dynamics, such as stochastic resonance, a phenomenon by which a system experiences a gain in signal-to-noise ratio (SNR) due to the addition of low amplitude noise. In thisthe experimental setup, inspired by the system proposed in Donoso, Ladera, Eur. J. Phys. 33 (2012), a magnet on a spring oscillates in the magnetic field of a small coil while a larger coil at the base of the setup drives the system with an oscillating magnetic field. The bistable nature of the system’s potential energy allows noise-induced phase transitions between potential wells corresponding to a Kramers’ rate for the system. In this presentation, we show progress on an experimental study of this rate of transition (Kramers’ rate) and compare obtained experimental results with the theoretical value of the system’s Kramers’ rate. In addition, we present new experimental data showing stochastic resonance behavior of the SNR dependence on the value of the amplitude of an external force.