Recently, emphasis in modelling ULF pulsations has begun to shift away from steady-state driving mechanisms towards impulsive and non-steady sources. We propose a model allowing numerical solution of the coupled hydromagnetic wave equations with arbitrary azimuthal asymmetry in a cylindrical magnetospheric geometry. General time-dependent stimuli can be applied at the outer (magnetopause) boundary, an arbitrary Alfv¿n speed distribution can be defined within the boundary, and ionospheric Joule dissipation is included. Initial results are presented which show that impulsive stimuli at the magnetopause can set up compressional cavity resonances which drive transverse field-line resonances within the magnetosphere, in general agreement with recent predictions. For a realistic ionospheric dissipation, and azimuthal wavenumber ~3, it is found that transient transverse mode solutions are of comparable importance to monochromatic solutions near the resonant field line.