The problem of the shift and broadening of the normal modes of electromagnetic oscillations in a cylindrical cavity resonator with axisymmetric interior and ideally conducting walls with a circular hole at the base is solved. It is shown that the existence of the hole perturbs the normal frequencies, and this perturbation is calculated. The method of solution is based on the Rayleigh-Schrodinger perturbation theory. It is found that the frequency shift depends on the value of the perturbed electric field at the hole. This field is calculated using the quasistatic approximation, which involves the solution of a mixed boundary value problem for the potential. An expression for the frequency shift and broadening is obtained.
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