For a certain class of magnetic field time geometries and for an arbitrary distribution of the plasma density used as a model for the earth's magnetosphere, we study the conditions under which resonantly enhanced Alfv¿n oscillations may occur. By calculating the field-aligned integral of the energy density flux, it is demonstrated that these oscillations are associated with localized energy absorption and are driven by gradients of the field-aligned component of the magnetic wave field. The results are generalized to account for a finite conductivity of the ionosphere. Finally, it is shown that a lack of symmetry of the mgnetosphere may cause the polarization of the resonant oscillation to conflict with the requirement for the wave field to be almost incompressible and thereby prevent the resonance absorption. We discuss probable consequences on the occurrence probability of ULF pulsations with magnetic local time.