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In this paper, we are interested in using impedance boundary conditions ( IBCs) to model the scattering from a vibrating object which can be considered a perturbation problem where the perturbation (and the corresponding IBC) varies with time. One of the most basic objects for which a scattering solution can be obtained is an infinite PEC cylinder. Using the exact solution for a circular cylinder, the IBCs needed to model the scattering from a perturbed PEC cylinder are derived for both the TM and TE polarizations. It is shown that the standard IBC (SIBC) is accurate to first order for the TM case, but a second generalized IBC (GIBC) is needed to provide first order accuracy for the TE case. Results from a moments method (MoM) implementation of the IBCs are presented.