Complex-exponential representation of time-domain response of a one-mode resonator

Time-domain response of a one-mode resonator is investigated by using a complex-exponential representation of the time-domain impulse response. The transient response of a resonator has calculated for a short incident pulse which has rectangular form and the radio frequency filling. The convolution integral has been analytically carried out and two solutions for the time histories of the transient response of the resonator have been found. They are the early-time and late-time portions of the signal. The behaviour of amplitude and frequency of the transient response of the electrodynamical structure under consideration is studied.