Vibrations and Waves

The Manchester Physics Series
General Editors: F.K. Loebinger; F. Mandl; D.J. Sandiford
School of Physics and Astronomy, The University of Manchester
Properties of Matter
B.H. Flowers and E Mendoza
Statistical Physics: Second Edition F. Mandl
Electromagnetism: Second Edition I.S. Grant and W.R.Phillips
Statistics R.J. Barlow
Solid State Physics: Second Edition J.R. Hook and H.E. Hall
Quantum Mechanics F. Mandl
Computing for Scientists R.J. Barlow and A.R. Barnett
The Physics of Stars: Second Edition A.C. Phillips
Nuclear Physics J.S. Lilley
Introduction to Quantum Mechanics A.C. Phillips
Particle Physics: Third Edition B.R. Martin and G. Shaw
Dynamics and Relativity J.R. Forshaw and A.G. Smith
Vibrations and Waves G.C. King
Vibrations and Waves is based on an introductory course given regularly by the author. The text provides the student with a thorough grounding in the theory of vibrations and waves.
Throughout the book, the fundamental principles of vibrations and waves are emphasised so that these principles can be applied to a wide range of oscillating systems and to different kinds of waves.
The text, which is divided into two sections, vibrations followed by waves, follows a logical progression from the simple harmonic oscillator to waves in continuous media.
Vibrations and Waves includes:
Vibrations and waves beautifully and concisely described in terms of the mathematical equations used throughout the bookWorked examples throughoutProblems ranging in difficulty from simple to challenging
Solutions and hints to the problems at the end of the book

Spis treści:
Editors’ Preface to the Manchester Physics Series.
Author’s Preface.
1 SIMPLE HARMONIC MOTION.
1.1 Physical Characteristics of Simple Harmonic Oscillators.
1.2 A Mass on a Spring.
1.2.1 A mass on a h orizontal spring.
1.2.2 A mass on a vertical spring.
1.2.3 Displacement, velocity and acceleration in simple harmonic motion.
1.2.4 General solutions for simple harmonic motion and the phase angle φ.
1.2.5 The energy of a simple harmonic oscillator.
1.2.6 The physics of small vibrations.
1.3 The Pendulum.
1.3.1 The simple pendulum.
1.3.2 The energy of a simple pendulum.
1.3.3 The physical pendulum.
1.3.4 Numerical solution of simple harmonic motion3.
1.4 Oscillations in Electrical Circuits: Similarities in Physics.
1.4.1 The LC circuit.
1.4.2 Similarities in physics.
PROBLEMS 1.
2 THE DAMPED HARMONIC OSCILLATOR.
2.1 Physical Characteristics of the Damped Harmonic Oscillator.
2.2 The Equation of Motion for a Damped Harmonic Oscillator.
2.2.1 Light damping.
2.2.2 Heavy damping.
2.2.3 Critical damping.
2.3 Rate of Energy Loss in a Damped Harmonic Oscillator.
2.3.1 The quality factor Q of a damped harmonic oscillator.
2.4 Damped Electrical Oscillations.
PROBLEMS 2.
3 FORCED OSCILLATIONS.
3.1 Physical Characteristics of Forced Harmonic Motion.
3.2 The Equation of Motion of a Forced Harmonic Oscillator.
3.2.1 Undamped forced oscillations.
3.2.2 Forced oscillations with damping.
3.3 Power Absorbed During Forced Oscillations.
3.4 Resonance in Electrical Circuits.
3.5 Transient Phenomena.
3.6 The Complex Representation of Oscillatory Motion.
3.6.1 Complex numbers.
3.6.2 The use of complex numbers to represent physical quantities.
3.6.3 Use of the complex representation for forced oscillations with damping.
PROBLEMS 3.
4 COUPLED OSCILLATORS.
4.1 Physical Characteristics of Coupled Oscillators.
4.2 Normal Modes of Oscillation.
4.3 Superposition of Normal Modes.
4.4 Oscillating Masses Coupled by Springs.
4.5 Forced Oscillations of Coupled Oscillators.
4.6 Transverse Oscillations.
PROBLEM S 4.
5 TRAVELLING WAVES.
5.1 Physical Characteristics of Waves.
5.2 Travelling Waves.
5.2.1 Travelling sinusoidal waves.
5.3 The Wave Equation.
5.4 The Equation of a Vibrating String.
5.5 The Energy in a Wave.
5.6 The Transport of Energy by a Wave.
5.7 Waves at Discontinuities.
5.8 Waves in Two and Three Dimensions.
5.8.1 Waves of circular or spherical symmetry.
PROBLEMS 5.
6 STANDING WAVES.
6.1 Standing Waves on a String.
6.2 Standing Waves as the Superposition of Two Travelling Waves.
6.3 The Energy in a Standing Wave.
6.4 Standing Waves as Normal Modes of a Vibrating String.
6.4.1 The superposition principle.
6.4.2 The superposition of normal modes.
6.4.3 The amplitudes of normal modes and Fourier analysis.
6.4.4 The energy of vibration of a string.
PROBLEMS 6.
7 INTERFERENCE AND DIFFRACTION OF WAVES.
7.1 Interference and Huygen’s Principle.
7.1.1 Young’s double–slit experiment.
7.1.2 Michelson spectral interferometer.
7.2 Diffraction.
7.2.1 Diffraction at a single slit.
7.2.2 Circular apertures and angular resolving power.
7.2.3 Double slits of finite width.
PROBLEMS 7.
8 THE DISPERSION OF WAVES.
8.1 The Superposition of Waves in Non–Dispersive Media.
8.1.1 Beats.
8.1.2 Amplitude modulation of a radio wave.
8.2 The Dispersion of Waves.
8.2.1 Phase and group velocities.
8.3 The Dispersion Relation.
8.4 Wave Packets.
8.4.1 Formation of a wave packet.
PROBLEMS 8.
APPENDIX: SOLUTIONS TO PROBLEMS.
Index.

Okładka tylna:
The Manchester Physics Series
General Editors: F.K. Loebinger; F. Mandl; D.J. Sandiford
School of Physics and Astronomy, The University of Manchester
Properties of Matter
B.H. Flowers and E Mendoza
Statistical Physics: Second Edition F. Mandl
Electromagnetism: Second Edition I.S. Grant and W.R.Philli ps
Statistics R.J. Barlow
Solid State Physics: Second Edition J.R. Hook and H.E. Hall
Quantum Mechanics F. Mandl
Computing for Scientists R.J. Barlow and A.R. Barnett
The Physics of Stars: Second Edition A.C. Phillips
Nuclear Physics J.S. Lilley
Introduction to Quantum Mechanics A.C. Phillips
Particle Physics: Third Edition B.R. Martin and G. Shaw
Dynamics and Relativity J.R. Forshaw and A.G. Smith
Vibrations and Waves G.C. King
Vibrations and Waves is based on an introductory course given regularly by the author. The text provides the student with a thorough grounding in the theory of vibrations and waves.
Throughout the book, the fundamental principles of vibrations and waves are emphasised so that these principles can be applied to a wide range of oscillating systems and to different kinds of waves.
The text, which is divided into two sections, vibrations followed by waves, follows a logical progression from the simple harmonic oscillator to waves in continuous media.
Vibrations and Waves includes:
Vibrations and waves beautifully and concisely described in terms of the mathematical equations used throughout the bookWorked examples throughoutProblems ranging in difficulty from simple to challenging
Solutions and hints to the problems at the end of the book