A dynamic analysis of free-piston Vuilleumier cycle heat pumps was carried out by a timestepping integration technique. The effects of external alternate force exciting a hot displacer piston upon the frequency response were taken into consideration as well as the viscous dissipation due to oscillating flow of working gas. We obtained a stable operation range in which the heat pump cycle is controllable and the cycle can be started with fairly small power on the external alternate force vs. operating frequency diagram. A mechanism to determine the amplitudes was explained based on the energy balance among the work done by the rod and by the dissipative and external forces. The internal force of the rod was found to play an important role in determining resonance frequencies.