Vibratory Motion Essay

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In its simplest form, vibration can be considered to be the oscillation or repetitive motion of an object around its equilibrium position. The equilibrium position is the position the object will attain when the force acting on it is zero. This type of vibration is called "whole body motion", meaning that all parts of the body are moving together in the same direction at any point in time.
The vibratory motion of a whole body can be completely described as a mixture of individual motions of six different types. These are presented in the three orthogonal directions x, y, and z, and rotation around the x, y, and z-axes. Any complex motion the body can be broken down into a combination of these six motions. Such a body is therefore said to have
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Free vibrations occur when the system is disturbed momentarily and then allowed to move without restraint. A classic example is provided by a weight suspended from a spring. In equilibrium, the system has minimum energy and the weight is at rest. If the weight is pulled down and released, the system will respond by vibrating vertically.
The vibrations of a spring are of a particularly simple kind known as simple harmonic motion (SHM). This occurs whenever the disturbance to the system is countered by a restoring force that is exactly proportional to the degree of disturbance. In this case, the restoring force is the tension or compression in the spring, which (according to Hooke’s law) is proportional to the displacement of the spring. In simple harmonic motion, the periodic oscillations are of the mathematical form called sinusoidal.
Most systems that suffer small disturbances counter them by exerting some form of restoring force. It is frequently a good approximation to suppose that the force is proportional to the disturbance, so that SHM is, in the limiting case of small disturbances, a generic feature of vibrating systems. One characteristic of SHM is that the period of the vibration is independent of its amplitude. Such systems therefore are used in regulating clocks. The oscillation of a pendulum, for instance, approximates SHM if the amplitude is

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