The mass-spring-damper model, shown in Figure 1.1, is the starting point for understanding mechanical vibrations. A thorough understanding of this most elementary vibration model and its full range of vibration characteristics is absolutely essential to a comprehensive and insightful study of the rotating machinery vibration field. The fundamental physical law governing all vibration phenomena is Newton’s Second Law, which in its most commonly used form says that the sum of the forces acting upon an object is equal to its mass times its acceleration. Both force and acceleration are vectors, so Newton’s Second Law, written in its general form, yields a vector equation. For the one-degree-of-freedom (1-DOF) system, this reduces to a scalar equation, as follows:

F = ma (1.1) where F is the sum of forces acting upon the body, m is the mass of the body, and a is the acceleration of the body.