A method for obtaining the time response of any linear system

A simple method is presented for obtaining the time response of any time-invariant linear system for zero or nonzero initial conditions and for inputs which can be expressed analytically. The method, in addition to its use in obtaining total solutions, is also useful in engineering education and industrial practice in learning how the basic types of transfer functions contribute to total system dynamics. Furthermore, as one's experience with this method increases, competence is gained in estimating the form of the total solution from an observation of the system transfer function and time input.