Introduction

The theory of vibration of single degree of freedom systems serves as one of the fundamental building blocks in the theory of vibration of discrete and continuous systems. As will be shown in later chapters, the concepts introduced and the techniques developed for the analysis of single degree of freedom systems can be generalized to study discrete systems with multi-degrees of freedom as well as continuous systems. For this volume to serve as an independent text, several of the important concepts and techniques used in the analysis of single degree of freedom systems are briefly discussed in this chapter. First, the methods of formulating the kinematic and dynamic equations are reviewed in the first three sections. It is also shown in these sections that the dynamic equation of a single degree of freedom system can be obtained as a special case of the equations of the multi-degree of freedom systems. The free vibrations of the single degree of freedom systems are reviewed in Sections 4 and 5, and the significant effect of viscous, structural, and Coulomb damping is discussed and demonstrated. Section 6 is devoted to the analysis of the forced vibrations of single degree of freedom systems subject to harmonic excitations, while the impulse response and the response to an arbitrary forcing function are discussed, respectively, in Sections 7 and 8.