Controlling the response of an oscillator using a coupled set of satellite oscillators

The response of a system comprised of multiple dynamic systems is analyzed. The results shown here are for the main or master oscillator in that system. The balance of the dynamic systems is designated as satellite oscillators. Controlling the response of the master oscillator is described in terms of the couplings to the master oscillator, the frequency distribution of the satellite oscillators, the loss factors, and the masses of those oscillators. The frequency distributions and masses of the satellite oscillators are specified via normalizations with respect to the resonance frequency and mass of the master oscillator in order to generalize the approach. It is shown that contrary to reported results by others, there is no requirement to optimize the frequency distribution of the satellite oscillators to maximize the control of the response of the master oscillator. Further it is shown that increasing the loss factor of the satellite oscillators beyond certain values does not bring further benefit in controlling the response of the master oscillator beyond a certain level, in fact, a saturation is reached. We describe the on-set of saturation in terms of the modal overlap parameter.