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
massless 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 
