This paper presents the vibrational characteristics of linear damped vibrational systems with a linear dynamic absorber. The amplitude ratios of main vibrational system are derived from the equation of motion for the system, and optimal natural frequency ratio and damping ratio of dynamic absorber are obtained by computer simu- lation, which minimize the amplitude ratio of main vibrational system for the whole range of the frequency ratio. And, the effects of the parameters on the amplitude ratios are investigated. As the results, the effect of the natural frequency ratio on the amplitude ratio of main vibrational system is more important than that of the damping ratio of dynamic absorber as damping ratio of main vibrational system becomes larger. For the case of large damping ration of main vibrational system becomes larger. For the case of large damping ratio of main vibration system, the amplitude ratios are not decreased dramationally in spite of inoreasing mass ratio.