The dynamics of rigidly rotating spiral waves under periodic modulation of excitability is studied experimentally in the photosensitive Belousov-Zhabotinsky reaction. The experiments of sinusoidal and pulsatory modulation reveal that the motion of the spiral tips can be forced to describe a wide range of cycloidal trajectories, depending strongly on the modulation period, The results are complemented with numerical simulations and discussed in the framework of the kinematical theory, We round that the critical parameter for a linear resonance drift under the periodic modulation is not only 'the modulation period', as reported earlier, but also the amplitude and duration of modulation. (c) 2005 Elsevier B.V. All rights reserved.