Abstract

In this paper, a new analysis technique for ordinary second-order systems is presented. The technique is based on multi-temporal conditions and results in a new closed-form for the complete response of second-order systems, which can be used to determine the complete solution of second-order systems with ease. In addition, the new technique provides a clear explanation of second-order systems, not only in the case of Direct Current (DC) forcing function but also in the case of time-varying function as well. By employing this new technique more accurate results with regard to response can be obtained which are compared to the result of the conventional technique. For example, amplitude of the natural response is shown to be a function of the forced response not only at the initial time but also at arbitrary points in time. Thus, for a constant forced function, which results in a constant forced response the results of the new technique is identical to the conventional technique, whereas in case of a time-varying forcing function the obtained response is different from the conventional technique. Numerical and experimental results obtained from the resistor-inductor-capacitor (RLC) circuit and the Wein bridge oscillator circuit show sufficient agreement with the theoretical results.

Key words: Second order system, multi temporal, new technique.