We use a normal-mode formalism to compute the response of a spherical, self-gravitating anelastic PREM-like Earth model to various excitation sources at the Slichter mode period. The formalism makes use of the theory of the Earth's free oscillations based upon an eigenfunction expansion methodology. We determine the complete response in the form of Green's function obtained from a generalization of Betti's reciprocity theorem. Surficial (surface load, fluid core pressure), internal (earthquakes, explosions) and external (object impact) sources of excitation are investigated to show that the translational motion of the inner-core would be best excited by a pressure acting at the core boundaries at time-scales shorter than the Slichter eigenperiods.