We consider a Brownian particle which is driven by a harmonically oscillating force, the motion of which is restricted by two reflecting boundaries. We solve the Fokker-Planck equation using the finite-element method and focus on the dynamics of the mean position of the particle in the time-asymptotic regime. As a function of the strength of the external force, the response of the system, i.e., the amplitude of the mean position and the dynamical shift, in the stationary limit shows a resonancelike behavior as a function of the diffusion coefficient for certain parameter regimes. We explain these numerical results heuristically and give some qualitative estimates.