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Linear time-varying (LTV) systems have found a niche of their own in the processing of continuous-time signals. In this brief, it is shown how the reduction of the duration of the transient response of a class of continuous-time LTV filters may be seen as the combined effect of the increased dampening of its amplitude response and the increase of the instantaneous frequency of its damped oscillations. For this aim, an LTV system whose damping factor and the damped frequency of its oscillations may be specified as functions of time is used as a vehicle of study. Time-varying eigenvalues are used to assess the behavior of the proposed system. Simulation results are used to verify the proposed mechanism behind the reduction of the duration of the transient response in the LTV filters under study.