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Chapter 2
The Kinematics of Vibration and Acoustics

## Excerpt

The motion represented by the equation

$y(t)=a0cosωt+b0sinωt$
or, in more compact complex variable notation,
$y(t)=a0eiωt$
is called simple harmonic motion. Most vibrations and noise we encounter belong to the category of linear vibration and consist of a linear combination of simple harmonic motions of different amplitudes, frequencies and phases. The frequency of a point mass-spring system is given by:
$ω=kmradian∕s$
The frequency in cycles/s, or Hz, is related to the frequency in radians/s by,
$f=ω2πHz$
The instantaneous velocity and acceleration of a vibrating point mass is given by:
$V(t)=ẏ(t)=iωy(t)$
$α(t)=ӱ(t)=−ω2y(t)$
The velocity of propagation of a wave is given by:
$c=fλ$
Vibrations can be represented in the time domain (time histories) or in the frequency domain (power spectral densities). Both contain the same information.

• Summary
• Nomenclature
• 2.1 Introduction
• 2.2 Free Vibration and Simple Harmonic Motion
• 2.3 Linear Vibration and Circular Motion
• 2.4 Vibration Measurement
• 2.5 Time Domain Representation of Vibration
• 2.6 Superposition of Sinusoidal Waves
• 2.7 Random Vibration and Noise
• 2.8 Frequency Domain Representation of Vibration
• 2.9 Traveling Waves
• 2.10 Propagation of Sound Waves
• Example 2.1: Tapping Wave Forms from Two Piston Lift Check Valves
• 2.11 Energy in Sound Waves
• 2.12 Threshold of Hearing and Threshold of Pain
• 2.13 The Logarithmic Scale of Sound Intensity Measurement—The Decibel
• 2.14 The Decibel Used in Other Disciplines
• 2.15 Case Studies
• Case Study 2.1: Forced Vibration of Nuclear Reactor Components by Coolant Pump-Generated Acoustic Load
• Case Study 2.2: Detecting Internal Leaks in a Nuclear Plant
• References
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