CHAPTER 2

Linear Physical Systems

Before the measurement and analysis of random physical data is discussed in more detail, it is desirable to clarify some pertinent concepts and fundamental definitions related to the dynamic behavior of physical systems. This chapter reviews the theoretical formulas for describing the response characteristics of ideal linear systems and illustrates the basic ideas for simple physical examples.

**2.1 CONSTANT-PARAMETER LINEAR SYSTEMS**

An ideal system is one that has *constant parameters* and is *linear* between two clearly defined points of interest called the input or excitation point and the output or response point. A system has constant parameters if all fundamental properties of the system are invariant with respect to time. For example, a simple passive electrical circuit would be a constant-parameter system if the values for the resistance, capacitance, and inductance of all elements did not change from one time to another. A system is linear if the response characteristics are additive and homogeneous. The term *additive* means that the output to a sum of inputs is equal to the sum of the outputs produced by each input individually. The term *homogeneous* means that the output produced by a constant times the input is equal to the constant times the output produced by the input alone. In equation form, if *f*(*x*) represents the output to an input *x*, then the system is linear if for any two inputs *x*_{1}, *x*_{2}, and constant *c*,

The constant-para ...