"Vibration is very common in engineering systems and forms and important subset of dynamics. We have already solved many vibration problems in the previous chapters, without calling specific attention to them... Vibration is the study of the repetitive motion of objects relative to some stationary frame of reference or nominal position (usually, the equilibrium position). Vibration is evident everywhere and in many cases greatly affects the nature of engineering design. The vibrational properties of engineering devices are often limiting factors in their performance. Vibration can be harmful and should then be avoided, or it can be extremely useful and desired. For instance, vibration induced in a building or car induces fatigue and failure. Yet vibration is purposely introduced by designers into certain machines used to sort parts and by musicians to create music." p561

AMPLITUDE
THE HEIGHT OF A WAVE

ANGULAR NATURAL FREQUENCY
THE NUMBER OF OSCILLATIONS PER SECOND THAT AN OBJECT ONDERGOES IN ITS NATURAL MOTION

FREQUENCY
A MEASURE OF HOW MANY TIMES A PHENOMENON REPEATS IN ONE UNIT OF TIME.

INITIAL CONDITIONS
THE VALUES THAT A SYSTEM HAS AT A STARTING MOMENT

LINEAR
PROPERTY OF SYSTEMS WHERE THE SYSTEM OUTPUT OR RESPONSE IS IN DIRECT PROPORTION TO THE INPUT. DOUBLING THE INPUT (LOAD, FORCE, ENERGY, TENSION,...) HAS THE EFFECT OF DOUBLING THE OUTPUT (STRETCH, COMPRESSION, DISPLACEMENT,...)

NATURAL FREQUENCY
THE NUMBER OF OSCILLATIONS PER UNIT OF TIME THAT AN OBJECT COMPLETES WHEN LEFT TO OSCILLATE NATURALLY WITH PERIODIC DRIVING FORCES.

NONLINEAR
A SYSTEM THAT DOES NOT FOLLOW THE LAW OF SUPERPOSITION. SUPERPOSITION IS TRUE IF YOU CAN MODEL THE COMPLEX SITUATION AS COMPOSED OF SIMPLER, BASIC SYSTEM. SUPPOSE A CAUSES B TO HAPPEN AND C CAUSES D TO HAPPEN. WHAT WILL OCCUR IF WE DO (A+C)? IN A NONLINEAR SYSTEM, (B+D) WILL NOT BE ALL OF THE OUTCOME.

PHASE
THIS WORD HAS MULTIPLE MEANINGS. SOLID, LIQUID AND GAS ARE THREE PHASES OF MATTER. CONCERNING OSCILLATING OR ROTATING OBJECTS, THE PHASE IS THE ANGULAR MEASURE (IN DEGREES OR RADIANS) OF THE LEAD AHEAD OR LAG BEHIND THAT AN OBJECT HAS WHEN IN MOTION.

STIFFNESS