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Acoustics and Mechanical Vibration General

Strength and Mechanics of Materials
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In Acoustics and Vibration, most periodic waves, regardless of the form , can be represented by two or more sine waves.  Most waves can be reduced to simple harmonic or sine wave components which generally form harmonic series. They have frequencies which are integral multiples of the lowest frequency. The lowest frequency is called the fundamental and the higher ones are called harmonic.

The Frequency of a vibrating body is the number of cycles of motion in a unit time.

The Period of a wave is the time elapsed while the motion repeats itself. It is the reciprocal of the frequency

The Amplitude of a wave is the shortest distance between twp particles along the wave which differ in phase by one cycle.

The number of independent coordinates necessary to describe the motion of a system is called the degrees of freedom. Examples of systems with various degrees of freedom with a mass "M" are shown below.

Example (D) is a single degree of freedom with a mass "m" supported on frictionless and mass-less rollers attached to a spring and a dashpot.


A) Single Degree of Freedom

B) Two Degrees of Freedom

C) Multiple Degrees of Freedom

D) One Degree of Freedom
Linear Vibration
Where:
m = Mass of the system
c = Coefficient of viscous damping
k = Spring constant
x = Displacement from rest
F(t) = Displacement as a function of time

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