Response of a Linear Oscillator to a Train of Forcing Functions

A noteworthy observation was made during an analog-computer investigation of the response of a vehicle suspension to a repetitive train of symmetrical forcing functions with differing time intervals between these impulses. It was found that a plot of the suspension displacement vs vehicle velocity of this single-degree-of-freedom system was dependent upon the direction of the vehicle velocity, i.e., the chronology of the train of the forcing functions. An inspection of the forcing function by the usual frequency analysis does not reflect this dependence on the chronology. This paper conveys the results of two analytical approaches to the problem of explaining the observation. For a linear system, the principle of superposition applies. The application of this principle in the frequency domain and in the time domain precipitates the characteristics of the forcing function on which the response is dependent.