Vibration is a major problem in space launch vehicles during burning sequences. These vehicles are vulnerable to impulsive and pulsed vibrations like those produced by rocket engines. The Ares I launch vehicle is anticipated to produce vibration in the organ pipe mode. The problems may be particularly severe if the pulses occur at the natural frequencies of the vehicle structure. In the case of the Ares, as the rocket burns, the excitation frequency drifts through the frequency corresponding to a longitudinal mode of the vehicle. Although it is not certain, there is concern that the corresponding vibrations are potentially severe enough as to be lethal to crew members and thus some consideration of vibration mitigation is warranted. Common approaches to dealing with vibration problems - structural redesign, addition of mass or damping materials - are not thought to be viable solutions; structural redesign through addition of mass and/or damping would result in excessive weights with corresponding performance limitations in terms of payload. The alternative approach is to retrofit the aft skirt with one or more tuned vibration absorbers (TVA). Application of an undamped TVA to a primary system introduces a zero in the frequency response of the primary system that is located at the TVA natural frequency. In the case of the Ares, however, the excitation frequency, while easily measured, is not fixed, but varies as the rocket burns. The effect of a TVA on the vibration of a primary system experiencing such an excitation is not known. The main objective of this research was to predict and simulate the behavior of a two degree of freedom (two-mass) system experiencing sinusoidal excitation with a linearly-varying frequency. In doing so, a framework for analyzing a primary system with a TVA implemented was realized. The resulting software was then used to model implementation of a specific TVA solution. Through analytical and simulated solutions, it was confirmed that a specific TVA could be used to effectively absorb the response at target frequencies when acted upon by a linearly changing oscillatory input.