The goal of this paper Is to characterize the vibration damping induced in a main structure by a large number of sub-oscillators. A simple expression is obtained for the substructure impedance when the number of sub-oscillators approaches Infinity. It is found that the induced damping depends on the total mass of the sub-oscillators resonating in a frequency band of interests and nearly independent of their Individual loss factors. A modal overlapping condition. which corresponds to bandwidths that exceed the spacing of those natural frequencies, is required for the sub-oscillators to have such effects. An impulse response of the system is also considered. When the sub-oscillators lack damping and do not satisfy the modal overlapping condition, the vibratory energy is returned from the sub-oscillators to the main structure at later times. The result of this paper is consistent with that found with the fuzzy structure and SEA framework.