  We use a simple model of Bullard-type disc dynamo, in which the disc rotation
rate is subject to harmonic oscillations, to analyze the generation of magnetic
field by the parametric resonance mechanism. The problem is governed by a
damped Mathieu equation. The Floquet exponents, which define the magnetic field
growth rates, are calculated depending on the amplitude and frequency of the
oscillations. Firstly, we show that the dynamo can be excited at significantly
subcritical disc rotation rates when the latter is subject to harmonic
oscillations with a certain frequency. Secondly, at supercritical mean rotation
rates, the dynamo can also be suppressed but only in narrow frequency bands and
at sufficiently large oscillation amplitudes.
