The Transient Response

It is often necessary to know the transient, or time domain behavior, of a system (such as the one depicted above). This is possible after a system model has been developed and a mathematical representation of the system obtained, it is (in the form of a differential equation, transfer function, ...).  The second page (ZI/ZS) describes how to use the Laplace Transform to solve a differential equation and then breaks the problem down into two parts (called the Zero Input and the Zero State responses).  The next page (Solution Methods) describes two common methods (Transfer Function Analysis and State Space Analysis for determining system response).  This is followed (Response to Inputs) by a description of the response to several commonly used system inputs, in particular the response of first and second order systems.  This is followed by (Relations...) a description of how the Transient Response is tied to the Frequency Response and other concepts.  While this information is not strictly necessary to determine the transient response, understanding these relationships give important insights into a system.  Finally, the transient response of systems that vibrate with no damping is covered; the response of such systems can use substantially different methods than those for systems with losses (i.e., damping).


© Copyright 2005 to 2015 Erik Cheever    This page may be freely used for educational purposes.

Erik Cheever       Department of Engineering         Swarthmore College