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We obtain the time-frequency response of the output of a dynamical system when the input belongs to a class of common nonstationary signals, namely, an impulse, a linear chirp, a causal sinusoid, and a short duration sinusoid. The obtained results clarify how the system processes the time-varying frequencies of the input signal to generate the time-frequency spectrum of the output. All analytic results are exact. The solution is obtained by developing a method which can be used to evaluate the output of a dynamical system for complex combinations of nonstationary inputs. We show numerical examples which prove that the response of a system to a nonstationary input is made by a series of events occurring in the joint time-frequency domain.