THE_PHYSICS_OF_VIBRATIONS_AND_WAVES_Sixt - THE PHYSICS OF...

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THE PHYSICS OF VIBRATIONSAND WAVESSixth EditionH. J. PainFormerly of Department of Physics,Imperial College of Science and Technology, London, UK
ContentsIntroduction to First Edition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xiIntroduction to Second Edition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xiiIntroduction to Third Edition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xiiiIntroduction to Fourth Edition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xivIntroduction to Fifth Edition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xvIntroduction to Sixth Edition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xvi1Simple Harmonic Motion1Displacement in Simple Harmonic Motion4Velocity and Acceleration in Simple Harmonic Motion6Energy of a Simple Harmonic Oscillator8Simple Harmonic Oscillations in an Electrical System10Superposition of Two Simple Harmonic Vibrations in One Dimension12Superposition of Two Perpendicular Simple Harmonic Vibrations15±Polarization17Superposition of a Large Numbernof Simple Harmonic Vibrations ofEqual Amplitudeaand Equal Successive Phase Differenced20±Superposition ofnEqual SHM Vectors of Lengthawith Random Phase22Some Useful Mathematics252Damped Simple Harmonic Motion37Methods of Describing the Damping of an Oscillator433The Forced Oscillator53The Operation of i upon a Vector53Vector form of Ohm’s Law54The Impedance of a Mechanical Circuit56Behaviour of a Forced Oscillator57v
Behaviour of Velocityvin Magnitude and Phase versus Driving Force Frequencyx60Behaviour of Displacement versus Driving Force Frequencyx62Problem on Vibration Insulation64Significance of the Two Components of the Displacement Curve66Power Supplied to Oscillator by the Driving Force68Variation ofPavwithx. Absorption Resonance Curve69TheQ-Value in Terms of the Resonance Absorption Bandwidth70TheQ-Value as an Amplification Factor71The Effect of the Transient Term744Coupled Oscillations79Stiffness (or Capacitance) Coupled Oscillators79Normal Coordinates, Degrees of Freedom and Normal Modes of Vibration81The General Method for Finding Normal Mode Frequencies, Matrices,Eigenvectors and Eigenvalues86Mass or Inductance Coupling87Coupled Oscillations of a Loaded String90The Wave Equation955Transverse Wave Motion107Partial Differentiation107Waves108Velocities in Wave Motion109The Wave Equation110Solution of the Wave Equation112Characteristic Impedance of a String (the string as a forced oscillator)115Reflection and Transmission of Waves on a String at a Boundary117Reflection and Transmission of Energy120The Reflected and Transmitted Intensity Coefficients120The Matching of Impedances121Standing Waves on a String of Fixed Length124Energy of a Vibrating String126Energy in Each Normal Mode of a Vibrating String127Standing Wave Ratio128Wave Groups and Group Velocity128Wave Group of Many Components. The Bandwidth Theorem132Transverse Waves in a Periodic Structure135Linear Array of Two Kinds of Atoms in an Ionic Crystal138Absorption of Infrared Radiation by Ionic Crystals140Doppler Effect1416Longitudinal Waves151Sound Waves in Gases151viContents
Energy Distribution in Sound Waves155Intensity of Sound Waves157Longitudinal Waves in a Solid159

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Term
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Tags
Simple Harmonic Motion, The Land, fixed length, electromagnetic waves

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