A Time Domain Interpretation of the Bode Plot For Instructional Purposes

In this note, the classical single input single output map (transfer function) as represented in the frequency domain, will be equivalently described in the time domain with gain and phase characteristics explicitly identified.This enables the educator to represent input-output maps in a purely time domain perspective, and clarify the complications introduced by using the Laplace operator and the frequency domain when analyzing system gain and phase portraits (Bode plots).A simple under damped externally driven bounded input bounded output stable differential equation will be used in this study.Comparisons in the time and frequency domain will be shown with examples, and possible assets for future classroom presentations will be discussed.