| In its simplest form, vibration can be
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| | other extreme of its displacement where
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| considered to be the oscillation or
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| | the spring will again begin to return it
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| repetitive motion of an object around an
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| | toward equilibrium. The same process
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| equilibrium position. The equilibrium
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| | repeats over and over with the energy
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| position is the position the object will
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| | sloshing back and forth between the spring
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| attain when the force acting on it is
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| | and the mass -- from kinetic energy in the
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| zero. This type of vibration is called
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| | mass to potential energy in the spring and
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| "whole body motion", meaning that all
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| | back.
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| parts of the body are moving together in
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| | The following illustration shows a graph
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| the same direction at any point in time.
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| | of the displacement of the mass plotted
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| The vibratory motion of a whole body can
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| | versus time.
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| be completely described as a combination
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| | If there were no friction in the system,
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| of individual motions of six different
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| | the oscillation would continue at the same
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| types. These are translation in the three
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| | rate and same amplitude forever.
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| orthogonal directions x, y, and z, and
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| | This idealized simple harmonic motion is
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| rotation around the x, y, and z-axes. Any
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| | almost never found in real mechanical
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| complex motion the body may have can be
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| | systems. Any real system does have
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| broken down into a combination of these
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| | friction, and this causes the amplitude of
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| six motions. Such a body is therefore said
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| | vibration to gradually decrease as the
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| to possess six degrees of freedom.
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| | energy is converted to heat. The following
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| For instance, a ship can move in the fore
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| | definitions apply to simple harmonic
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| and aft direction (surge), up and down
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| | motion: T = The period of the wave.
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| direction (heave), and port and starboard
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| | The period is the time required for one
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| direction (sway), and it can rotate
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| | cycle, or one "round trip" from one zero
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| lengthwise (roll), rotate around the
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| | crossing to the next zero crossing in the
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| vertical axis (yaw), and rotate about the
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| | same direction. The period is measured in
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| port-starboard axis (pitch).
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| | seconds, or milliseconds, depending on how
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| Suppose an object were restrained from
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| | fast the wave is changing.
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| motion in any direction except one. For
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| | A small compact physical structure, such
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| instance, a clock pendulum is restricted
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| | as a marble, can be thought of as simply a
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| from motion except in one plane. It is
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| | mass. It will move in response to an
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| therefore called a single degree of
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| | external force applied to it, and
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| freedom system. Another example of a
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| | Newton’s laws of motion will govern its
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| single degree of freedom system is an
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| | movement. Simply put, Newton's laws
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| elevator moving up and down in an elevator
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| | dictate that if the marble is at rest, it
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| shaft.
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| | will remain at rest unless acted on by an
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| The vibration of an object is always
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| | external force, and if in motion it will
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| caused by an excitation force. This force
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| | continue in motion unless acted on by an
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| may be externally applied to the object,
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| | external force. If it is subjected to an
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| or it may originate inside the object.
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| | external force, its acceleration will be
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| It will be seen later that the rate
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| | proportional to that force.
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| (frequency) and magnitude of the vibration
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| | Most mechanical systems are more complex
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| of a given object is completely determined
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| | than a simple mass, and they do not
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| by the excitation force, direction, and
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| | necessarily move as a whole when subjected
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| frequency. This is the reason that
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| | to a force. Mechanical systems, such as
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| vibration analysis can determine the
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| | rotating machines, are not infinitely
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| excitation forces at work in a machine.
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| | rigid, and have varying degrees of
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| These forces are dependent upon the
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| | flexibility at different frequencies. As
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| machine condition, and knowledge of their
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| | we will see, their motion in response to
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| characteristics and interactions allows
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| | an external force is dependent on the
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| one to diagnose a machine problem.
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| | nature of that force and the dynamic
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| The simplest possible vibratory motion
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| | characteristics of their mechanical
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| that can exist is the movement in one
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| | structure, and is often difficult to
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| direction of a mass controlled by a single
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| | predict. The disciplines of Finite Element
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| spring. Such a mechanical system is called
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| | Modeling (FEM) and Modal Analysis are
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| a single degree of freedom spring-mass
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| | dedicated to predicting how a structure
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| system. If the mass is displaced a certain
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| | will respond to a known force. We will not
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| distance from the equilibrium point and
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| | discuss these fields further, for they are
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| then released, the spring will return it
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| | very complex, but it is instructive to
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| to equilibrium, but by then the mass will
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| | look into how forces and structures
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| have some kinetic energy and will
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| | interact if we are to understand the
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| overshoot the rest position and deflect
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| | usefulness of vibration analysis of
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| the spring in the opposite direction. It
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| | machines.
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| will then decelerate to a stop at the
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