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- Augustana College- Rock Island
- Chapter 4: Vibrations

Karlie E.

complex vibration

any vibration consisting of the sum of more than one sinusoidal vibration

types of complex vibration

aperiodic

periodic

periodic

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fourier theorem

any complex oscillatory motion is the sum of various sinusoidal motions of varying amplitude, frequency and phase.

aperiodic vibration

a vibration without a repeating pattern in time

periodic vibration

a vibratory motion in which an object returns to the same point in space periodically during the motion

Fundamental period

The duration of one cycle of a complex periodic motion.

Equation for fundamental period

To= sec/cycles

Equation for fundamental frequency

fo= cycles/sec

Fundamental frequency

the lowest frequency of vibration

waveform synthesis

combining several individual sinusoidal motions into a complex waveform

how to determine waveform synthesis

add the instantaneous magnitudes of the different waveforms at any point in time

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Harmonics

frequency components of a complex waveform that are whole-number multiples of the fundamental frequency.

First Harmonic

is the fundamental frequency

Second Harmonic

component that is two times the fundamental frequency

Overtone

Vibration whose frequency is a multiple of the fundamental frequency; kind of like harmonics but up one step.

ex. first overtone = second harmonic

Greatest Common Factor GCF

The largest factor that 2 or more numbers have in common

Common Factor

number by which all the numbers in a given set can be divided without a remainder

Missing fundamental/ phantom fundamental

the components do not include a frequency equal to the GCF

Periodicity

the concept that a periodic wave keeps repeating itself for an infinite amount of time

Noise

random sequence of events resulting from the combination of a infinite number of unrelated components-- aperiodic waveform

Transient

brief single event that ceases to exist after a very short time (door slam)-- aperiodic waveform

Complex inharmonic vibration:

Waveform Analysis

breaking down a complex waveform to determine its individual components

Spectrum

graphical representation of a complex waveform showing the waveform energy (amplitudes) of the individual components arranged in order of frequency --- Graphical representation of the Fourier series of a complex vibration

Line Spectrum

when all complex waveforms result in a spectrum consisting of separate vertical lines-- both periodic and aperiodic vibrations

Continuous Spectrum

Spectrum appears as a filled in area (white noise)--infinite number of sinusoidal components

Amplitude spectrum

Amplitude by frequency, shows formants in peaks

Nodes

point on a vibrating system (string) where displacement remains zero-- attachment points

Antinodes

point at which the vibration magnitude is greatest-- on a string

Mode of vibration

the specific vibration pattern of a vibrating system associated with each resonance frequency of the system

Octave

doubling a frequency

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