Modelling of an Oscillatory Magnetic Field Action on a Ferrofluid Layer

We formulate the parametric resonance problem corresponding to an isothermal ferrofluid layer subjected to a magnetic field that consists of two parts. The first one is a vertical or a horizontal constant component. The second part is oscillating with time in a vertical plane. The Laplace law becomes then equivalent to the study of a Hill equation, thus generalizing the Mathieu equation studied for a purely oscillating magnetic field. This extends the classical Faraday vibrating problem to other experimental situations.