"Vibrations have been of concern in engineering at least since the beginning of the industrial revolution. The oscillatory motions of rotating and reciprocating engines subject their parts to large loads that must be considered in their design. Operators and passengers of vehicles powered by these engines must be isolated from their vibrations. Beginning with the development of electromechanical devices capable of creating and measuring mechanical vibrations, such as speakers and microphones, engineering applications of vibrations have included the various areas of acoustics, from architectural acoustics to earthquake detection and analysis. In this chapter we consider vibrating systems with one degrree of freedom; that is, the position, or each configuration, of each system is specified by a single variable. Many actual vibrating systems either have only one degree of freedom or their motions can be modeled by a one-degree-of-freedom system in particular circumstances. We discuss fundamental concepts, including amplitude, frequency, period, damping, and resonance, that are also used in the analysis of systems with multiple degrees of freedom." p483

DIFFERENTIAL EQUATION
AN EQUATION THAT RELATES THE RATES OF CHANGE OF DIFFERENT PROCESSES OR PHYSICAL PARAMETERS.

EQUATION
A MATHEMATICAL EQUALITY RELATING PARAMETERS OR MEASUREMENTS

EQUILIBRIUM
A STEADY-STATE CONDITION IN WHICH FORCES, TORQUES, FLOWS MAY BE HAPPENING BUT THE SYSTEM UNDER STUDY IS NOT CHANGING WITH TIME.

EQUILIBRIUM
A STATE OF BALANCE. FORCES, MOMENTS, FLOWS MAY BE OCCURRING IN A SYSTEM BUT NO NET CHANGE IS OCCURRING IN THE SYSTEM.

EQUILIBRIUM POSITION

EQUILIBRIUM POSITION
THIS IS THE CONFIGURATION OR POSITION OF AN OBJECT IN WHICH THE SUM OF MOMENTS (TORQUES) ON AN OBJECT IS ZERO AND THE SUM OF FORCES ON AN OBJECT IS ZERO. AN OBJECT PLACED AT REST IN ITS EQUILIBRIUM POSITION OR CONFIGURATION WILL REMAIN IN THAT STATE.

ONE DEGREE OF FREEDOM
THE MOTION OF AN OBJECT WITH ONE DEGREE OF FREEDOM CAN BE COMPLETELY DESCRIBED WITH ONE POSITION COORDINATE. OFTEN, SYSTEMS WITH ONE DEGREE OF FREEDOM ARE CAPABLE OF ONLY STRAIGHT LINE MOTION.

ORDINARY DIFFERENTIAL EQUATION
A CERTAIN KIND OF EQUATION THAT RELATES RATES OF CHANGE FOR A SYSTEM TO EACH OTHER.

PENDULUM
AN OBJECT ATTACHED BY A LIGHT WIRE OR STRING TO A SUPPORT THAT SWINGS BACK AND FORTH UNDER THE PULL OF GRAVITY.

POSITION
A POINT IN SPACE. COORDINATES ARE THE NUMBERS USED TO SPECIFY THE POSITION OF THE POINT IN SPACE.