ABSTRACT
The vibrations or oscillations of mechanical systems constitute one of the most important fields of study in all physics. Virtually every system possesses the capability for vibration, and most systems can vibrate freely in a large variety of ways. A thorough familiarity with sinusoidal vibrations will open the door to every conceivable problem involving periodic phenomena. The feature that all such phenomena have in common is periodicity. There is a pattern of movement or displacement that repeats itself over and over again. One of the most useful ways of describing simple harmonic motion is obtained by regarding it as the projection of uniform circular motion. The use of a uniform circular motion as a purely geometrical basis for describing simple harmonic motion embodies more than physicists have so far chosen to recognize. There exists an unambiguous way of establishing and maintaining the distinction between the physically real and the physically unreal components of the motion.
