Introduction

We now develop methods for calculating the dynamic response of a linear system that is modeled by its transfer functions. The response depends upon the physical parameters of the system, the input function, and any nonzero initial conditions. We are particularly interested in relating the dynamic features of the response to the physical properties of the system. If the input is a step function, the response may fluctuate temporarily and eventually reach a constant value. The nature of the fluctuations – the length of time during which they persist, and whether they cause the response to overshoot its final value excessively or to oscillate with both positive and negative values – are dynamic features of vital importance. The initial values of the response and its derivatives and the final value of the response are also important characteristics that depend on the physical parameters. In simple systems with simple inputs – for example, a firstor second-order system with a step input – the dynamic features of the response are directly related to simple combinations of the parameter values. But in higher-order systems these important relationships are less obvious because the significant dynamic features of the response depend on complicated combinations of the parameter values. We must now employ a mixture of analysis tools, computer calculations, and approximation techniques to determine which of our system parameters have the most influence on the significant dynamic features of the response.