ABSTRACT
This chapter discusses linear system theory and the basic properties of linear systems, and establishes notation. For linear systems, the steady-state response to a periodic force is periodic with the same frequency, but not necessarily in phase due to the energy dissipation by the damping term which causes the output to lag the input. It has been proved useful to consider a two degree-of-freedom system to discuss how natural frequencies etc. generalize to multi-degree-of-freedom systems. However, as one might expect, it is possible to deal with linear systems with arbitrary numbers of degree-of-freedom at the expense of a little more abstraction. The chapter formalizes the arguments for multi-degree-of-freedom systems and states them in their full generality. It provides the theory of an undamped unforced system. All the system invariants taken for granted for a linear system—resonant frequencies, damping ratios, modeshapes, frequency response functions—become dependent on the level of the excitation applied during the test.
