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A first course in vibrations and waves / Mohammad Samiullah

Author
Samiullah, Mohammad
Published
Oxford : Oxford University Press, 2015.
Copyright Date
©2015
Edition
First edition.
Physical Description
xiii, 492 pages : illustrations ; 25 cm

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Contents
Machine generated contents note: 1.Review of Mechanics and Complex Algebra -- 1.1.Review of Mechanics -- 1.1.1.Kinematics -- 1.1.2.Dynamics: Newton's Laws of Motion -- 1.1.3.Work, Energy, and Power -- 1.1.4.Conservation Laws -- 1.2.Complex Numbers -- 1.2.1.The Complex Plane -- 1.2.2.The Exponential Form -- 1.2.3.Complex Algebra -- 1.2.4.Complex Exponential Function of Time -- 1.2.5.Vibrations and Complex Functions -- 1.2.6.Adding Two Sinusoidal Vibrations-Beat Phenomenon -- 1.2.7.Complex Exponentials and Equations of Motion -- Exercises -- 2.Free Oscillations-One Degree of Freedom -- 2.1.Basic Characteristics of an Oscillatory Motion -- 2.2.Stable Equilibrium and Restoring Force -- 2.3.Free Oscillations of a Mass/Spring System -- 2.3.1.Solving the Equation of Motion -- 2.3.2.Specifying Initial Position and Velocity -- 2.3.3.Physical Meaning of ω -- 2.3.4.Physical Meaning of Phase Constant, φ -- 2.4.Energy of a Simple Harmonic Oscillator -- 2.5.Other Examples of Simple Harmonic Motion -- 2.5.1.Plane Pendulum -- 2.5.2.Torsion Pendulum -- 2.5.3.Physical Pendulum -- 2.5.4.Oscillations of Freely Floating Objects -- 2.5.5.Electromagnetic Oscillations in LC Circuits -- 2.6.Simple Harmonic Motion Near Potential Minima -- 2.7.Damping of Oscillations -- 2.7.1.Solving the Equation of Motion -- 2.7.2.Dissipation of Energy and the Quality of an Oscillator -- 2.8.The Damped AC Circuit -- Exercises -- 3.Coupled Oscillations-Two Degrees of Freedom -- 3.1.Linear Systems and Normal Modes -- 3.2.Two Coupled Pendulums -- 3.2.1.Guessing the Normal Modes -- 3.2.2.General Motion Using Normal Coordinates -- 3.3.Systematic Method for Normal Modes -- 3.3.1.The Double Pendulum -- 3.3.2.Summary of Steps for Obtaining Normal Modes -- 3.4.Matrix Methods -- 3.4.1.Eigenvectors and Eigenvalues -- 3.5.Longitudinal Vibration Modes -- 3.6.Transverse Vibrations -- 3.7.Energy of Coupled Systems and Normal Coordinates -- 3.8.Coupled Electrical Oscillators -- 3.9.Damped Coupled Systems -- Exercises -- 4.Systems with Many Degrees of Freedom -- 4.1.Transverse Oscillations of Beads on a String -- 4.1.1.Normal Modes -- 4.1.2.General Solution -- 4.2.The Normal Modes in the Continuum Limit -- 4.3.Vibrations of a Taut String-Continuum Model -- 4.3.1.Derivation of Wave Equation -- 4.3.2.Modes of a String Fixed at Both Ends -- 4.4.Transverse Oscillations of a String Free at One End -- 4.4.1.The Modes of a String with Both Ends Free -- 4.5.Longitudinal Oscillations -- 4.5.1.Stress and Strain -- 4.5.2.Longitudinal Vibrations in a Rod -- 4.6.Vibrations of an Air Column -- 4.7.Vibrations of Two- and Three-Dimensional Systems -- 4.7.1.Transverse Oscillations of a Rectangular Plate -- 4.7.2.Free Vibrations of a Drum -- 4.8.Fourier Analysis -- 4.8.1.Fourier Series -- 4.8.2.Fourier Analysis in Terms of Normal Modes -- 4.8.3.Dynamics of Taut String Using Modes -- Exercises -- 5.Driven Oscillations -- 5.1.Damped Driven One-dimensional Harmonic Oscillator -- 5.2.Steady State Solution -- 5.2.1.Amplitude and Phase Constant in Steady State -- 5.2.2.Complex Exponential Method for Steady State Solution -- 5.2.3.Absorptive and Elastic Amplitudes -- 5.2.4.Power of the Driving Force -- 5.2.5.Resonance Curve of Power -- 5.2.6.Variation of the Elastic and Absorptive Amplitudes with Frequency -- 5.2.7.Variation of Amplitude and Phase Constant with Frequency -- 5.3.Transient Solution -- 5.3.1.General Solution -- 5.4.Resonance in Coupled Systems -- 5.4.1.Normal Modes and Harmonic Driving Force -- 5.4.2.Power and Normal Modes -- 5.5.Driving a Coupled System with Many Degrees of Freedom -- 5.5.1.Upper and Lower Cutoffs -- 5.5.2.Solving Multi-particle Systems -- 5.5.3.Driving Continuous Systems -- 5.6.Electrical Resonance-RLC circuit -- 5.6.1.Single Variable Driven Circuit -- 5.6.2.Electrical Filters and Driven Coupled Circuits -- 5.6.3.Driven LC Network -- Exercises -- 6.Traveling Waves in One Dimension -- 6.1.Harmonic Traveling Waves -- 6.2.Standing Waves -- 6.2.1.Similarities and Differences Between Standing Waves and Traveling Waves -- 6.3.Dispersion and Group Velocity -- 6.4.Energy Transport by Traveling Wave -- 6.4.1.Energy in a Wave -- 6.4.2.Power of the Wave Generator -- 6.5.Traveling Wave in a Transmission Line -- 6.6.Superposition of Harmonic Waves -- 6.6.1.Beats in Waves of Two Different Frequencies -- 6.6.2.Superposition of N Harmonic Waves -- 6.7.Spectrum Analysis of Waves -- 6.7.1.Non-harmonic Periodic Waves -- 6.7.2.Nonperiodic Pulses and Fourier Integral Technique -- 6.8.Doppler Effect -- 6.8.1.Non-relativistic Doppler Effect -- 6.8.2.Relativistic Doppler Effect -- 6.8.3.Doppler Effect and Aberration -- 6.8.4.Ives-Stilwell Experiment -- Exercises -- 7.Waves in Three-Dimensional Space -- 7.1.Waves in Three Dimensions -- 7.1.1.Harmonic Waves -- 7.1.2.Plane Traveling Harmonic Waves in Three Dimensions -- 7.1.3.Wavefront and Phase Velocity -- 7.1.4.Spherical Traveling Harmonic Wave -- 7.1.5.Mixed Harmonic Waves -- 7.2.Acoustic Waves in Fluids -- 7.2.1.Acoustic Wave Equation in Fluid -- 7.2.2.Plane Acoustic Wave -- 7.2.3.Intensity of Acoustic Waves -- 7.2.4.Pressure and Displacement Waves -- 7.2.5.Standing Acoustic Waves in One Dimension -- 7.2.6.Standing Acoustic Waves in Three Dimensions -- 7.3.Electromagnetic Waves -- 7.3.1.Maxwell's Equation in a Vacuum and the Electromagnetic Wave Equation -- 7.3.2.Plane Harmonic Electromagnetic Wave -- 7.3.3.Intensity of Electromagnetic Wave -- 7.3.4.Electromagnetic Momentum and Radiation Pressure -- 7.3.5.Polarization of an Electromagnetic Wave -- 7.4.Matter Waves -- 7.4.1.Free particle in Open Space -- 7.4.2.Free Particle in a Confined Space -- 7.5.Shock Waves -- Exercises -- 8.Reflection and Transmission of Waves -- 8.1.Waves in Different Media -- 8.1.1.Wavelengths in Different Media -- 8.1.2.Boundary Conditions at the Junction of Two Media -- 8.2.Reflection and Transmission of Waves -- 8.2.1.Reflection and Transmission Coefficients -- 8.2.2.Perfect Reflection -- 8.2.3.Perfect Termination and Impedance Matching -- 8.3.Scattering of a Wave from a Mass on the String -- 8.4.Reflection of Electromagnetic Waves -- 8.4.1.Transverse Electric (TE) Case -- 8.4.2.Fresnel's Equations for the Transverse Magnetic (TM) Case -- 8.4.3.Consequences of Fresnel's Equations -- Exercises -- 9.Interference -- 9.1.The Superposition Principle -- 9.1.1.Linearity of Wave Equation -- 9.1.2.Intensity and Superposition Principle -- 9.2.The Interference Between Two Point Sources -- 9.2.1.The Derivation of Net Intensity at a Detector -- 9.2.2.Interference Conditions in Terms of Direction -- 9.2.3.Identical Sources -- 9.2.4.Energy Conservation -- 9.2.5.Interference Conditions for Sources with Phase Difference -- 9.2.6.Interference Hyperboloids -- 9.2.7.Coherence and the Interference Pattern -- 9.3.Interference Experiments -- 9.3.1.Wavefront-splitting and Young's Double Slit Experiment -- 9.3.2.Amplitude-splitting and Double-Beam Interference -- 9.4.Practical Applications of Interference -- 9.4.1.Michelson Interferometer -- 9.4.2.Fabry-Perot Interferometer -- Exercises -- 10.Diffraction -- 10.1.Huygens-Fresnel Principle -- 10.2.Diffraction through a Single Slit -- 10.2.1.Near-Field versus Far-Field -- 10.2.2.Calculation of Intensity in the Far-Field Region -- 10.2.3.The Maxima and Minima of the Diffraction Pattern -- 10.3.Diffraction through a Circular Aperture -- 10.3.1.The Diffraction Pattern -- 10.3.2.Limitations on Imaging Due to Diffraction -- 10.4.Fraunhofer Diffraction through a Double Slit -- 10.4.1.The Diffraction Pattern -- 10.4.2.Derivation of the Intensity Formula -- 10.5.Diffraction Grating -- 10.5.1.Principal Maxima -- 10.5.2.Angular Width of Principal Maxima -- 10.5.3.Resolving Power -- Exercises.
Summary
The book contains a detailed treatment of vibrations and waves at an introductory level. Since waves appear in almost all branches of physics and engineering, readers will be exposed to different types of waves in this book with a common language.
The study of vibrations and waves is central to physics and engineering disciplines.This text contains a detailed treatment of vibrations and waves at an introductory level suitable for second and third year students. It builds on first year physics and emphasizes understanding of vibratory motion and waves based on first principles. Since waves appear in almost all branches of physics and engineering, readers will be exposed to many different types of waves; this study aims to draw together their similarities, by examining them in a common language. The book is divided into three parts: Part I contains a preliminary chapter that serves as a review of relevant ideas of mechanics and complex numbers. Part II is devoted to a detailed discussion of vibrations of mechanical systems. This part covers simple harmonic oscillator, coupled oscillators, normal coordinates, beaded string, continuous string, and Fourier series. It concludes with a presentation of stationary solutions of driven finite systems. Part III is concerned with waves, focusing on the discussion of common aspects of all types of waves, and the applications to sound, electromagnetic, and matter waves are illustrated. Finally, relevant examples are provided at the end of the chapters to illustrate the main ideas, and better the reader's understanding.
Subject(s)
ISBN
9780198729792 (pbk.)
0198729790 (pbk.)
9780198729785 (hbk.)
0198729782 (hbk.)
Note
Includes index.
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