Abstract
In this paper, it was analytically made clear that solutions for the impact oscillator systems have accurate recursive feedback structural properties. First, solutions previously obtained in terms of self-reference was replaced by those which do not have explicit terms of impact velocity. As a result of this procedure, solutions in the of reference value decomposition was achieved in which explicit expression of the equation was obtained by taking the impact time as only parameter. Secondly, this formulation was furthermore developed by proposing the analytical procedure for getting general solutions of recurrence form which can lead the solutions expressed by the impact recurrence. From this formulation, it was exactly clarified that these solutions have recursive feedback structural property with respect to the impact. Finally, through the formulation proposed in this examination, a kind of binary-tree structure can be recognized in the linear system transform from the velocity domain into the time domain when we get the pseudo-feedback response solutions.
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