Absorption of magnetosonic cavity modes by excitation of the spatial Alfve´n resonance and by resonant particle absorption (transit time magnetic pumping) are studied and the strengths of the two damping mechanisms compared. For the mode studied, the poloidal mode number is low. This implies that the magnetosonic turning point is close to the Alfve´n resonance. To deal with the resulting differential equation an asymptotic expansion technique is utilized, first using ideal magnetohydrodynamic equations, and, subsequently, with finite ion Larmor radius effects included. The antenna impedance and cavityQare studied as a function of plasma and antenna parameters. It is found that either Alfve´n resonance or resonant particle absorption dominate depending principally on radial mode number.