Introduction ................................................... xi
Chapter 1. Simple Harmonic Motion, Damping and Resonance ....... 1
1.1 Simple Harmonic Motion ..................................... 1
1.1.1 A mass on a vertical spring ......................... 1
1.1.2 The simple pendulum ................................. 4
1.1.3 The energy of simple harmonic motion ................ 5
1.2 Damped Simple Harmonic Motion .............................. 7
1.2.1 Light damping ....................................... 8
1.2.2 Heavy damping ....................................... 9
1.2.3 Critical damping ................................... 10
1.3 Forced Vibration and Resonance ............................ 11
Problems 1 ................................................ 14
Chapter 2. Resonance in Everyday Life .......................... 17
2.1 A Girl on a Swing ......................................... 17
2.2 The Opera Singer and the Wine Glass ....................... 18
2.3 Bridges ................................................... 20
2.3.1 The Broughton Suspension Bridge .................... 21
2.3.2 The Millennium Bridge, London ...................... 22
2.4 Washboard Roads ........................................... 23
2.5 Buildings and Earthquakes ................................. 25
2.6 Resonance and Musical Instruments ......................... 27
2.6.1 Resonance of air in a pipe ......................... 27
2.6.2 Resonance in a string .............................. 31
2.6.3 The violin ......................................... 32
Chapter 3. Electrical Circuits and Resonance .................. 35
3.1 Direct-Current Circuits ................................... 35
3.2 Expressing an Alternating Potential Difference ............ 36
3.3 Complex Impedances ........................................ 37
3.3.1 Inductors .......................................... 37
3.3.2 Capacitors ......................................... 39
3.4 A Series LCR Resonance Circuit ............................ 41
3.5 A Parallel LCR Resonance Circuit .......................... 43
Problems 3 ................................................ 47
Chapter 4. Resonance in the Solar System ....................... 49
4.1 Kirkwood Gaps ............................................. 49
4.2 Saturn's Rings ............................................ 54
4.3 Volcanoes on the Satellite Io ............................. 58
4.3.1 Elastic hysteresis and Q values .................... 59
4.3.2 Elliptical orbits . . .............................. 60
4.3.3 The generation of energy in Io by tidal stressing .. 62
4.4 Commensurabilities of Planetary and Satellite Orbits ...... 65
4.4.1 Planetary commensurabilities ....................... 65
4.4.2 The commensurabilities of the Galilean satellites .. 70
4.4.3 The commensurabilities of some of Saturn's
satellites ......................................... 72
4.4.4 The Trojan asteroids ............................... 74
Problems 4 ................................................ 78
Chapter 5. Nuclear Magnetic Resonance ......................... 81
5.1 A Brief Review of the Structure of Atoms .................. 81
5.2 Intrinsic Spins and Magnetic Moments ...................... 82
5.2.1 Orientation of nuclei in a magnetic field .......... 84
5.3 Magnetic Resonance Imaging (MRI) .......................... 87
5.3.1 Larmor precession .................................. 88
5.3.2 The basic physics of the МЫ process ................ 91
5.3.3 Fourier transforms ................................. 95
5.3.4 The MRI procedure .................................. 97
5.4 Other Applications of NMR ................................ 102
Problems 5 ............................................... 102
Chapter 6. Electron Spin Resonance ............................ 105
6.1 The Electronic Structure of Molecules and Free Radicals .. 105
6.1.1 The electronic structure of atoms ................. 105
6.1.2 The electronic structure of molecules ............. 108
6.1.3 The electronic structure of free radicals ......... 110
6.2 The Basic Theory of Electron Spin Resonance .............. 111
6.3 The Form and Use of an ESR Spectrometer .................. 114
6.4 ESR Spectra .............................................. 115
6.4.1 ESR spectra for a single neighbouring nucleus
with nuclear spin ................................. 116
6.4.2 Many nuclei in equivalent positions ............... 119
6.4.3 Two sets of non-equivalent nuclei ................. 120
Problems 6 ............................................... 122
Chapter 7. Resonance with Electromagnetic Radiation ........... 123
7.1 Fraunhofer Lines ......................................... 123
7.1.1 Energy levels in atoms ............................ 123
7.1.2 Atomic spectra .................................... 124
7.1.3 Formation of Fraunhofer lines ..................... 126
7.2 Lasers ................................................... 126
7.2.1 Spontaneous and stimulated emission ............... 127
7.2.2 A simple laser system and uses of lasers .......... 130
7.3 Radar .................................................... 131
7.3.1 The klystron amplifier ............................ 133
7.3.2 The cavity magnetron .............................. 135
7.4 The Anomalous Scattering of X-rays ....................... 136
7.4.1 Scattering from a free electron ................... 137
7.4.2 Scattering from a bound electron .................. 138
Problems 7 ............................................... 143
Chapter 8. Nuclear Physics, Radiation and Particle Physics .... 145
8.1 The Beginning of Nuclear Physics ......................... 145
8.2 The Cockcroft-Walton Experiment .......................... 147
8.3 The Cyclotron ............................................ 149
8.3.1 Maintaining resonance ............................. 153
8.3.2 Overcoming special relativity effects ............. 154
8.4 Linear Particle Accelerators ............................. 155
8.5 Synchrotrons ............................................. 157
8.6 Particles and Particle Colliders ......................... 160
8.6.1 The neutrino ...................................... 161
8.6.2 Leptons ........................................... 161
8.6.3 Quarks and sub-atomic particles ................... 162
8.6.4 Particle colliders ................................ 164
Problems 8 ............................................... 166
Chapter 9. The Mossbauer Effect ............................... 169
9.1 The Basis of the Mossbauer Effect ........................ 169
9.2 Natural Line-Widths ...................................... 169
9.3 Doppler Broadening ....................................... 170
9.4 The Effect of Recoil ..................................... 172
9.5 Nuclear Emission of γ-rays ............................... 174
9.6 Factors Affecting γ-Ray Emission ......................... 175
9.6.1 Natural line-width for γ-rays ..................... 175
9.6.2 Doppler line broadening for γ-rays ................ 176
9.6.3 The recoil frequency shift for γ-rays ............. 176
9.7 Mossbauer Spectroscopy ................................... 177
9.7.1 Experimental equipment ............................ 178
9.8 Spectral Features ........................................ 179
9.8.1 Isomer shift ...................................... 180
9.8.2 Quadrupole splitting .............................. 180
9.8.3 Magnetic splitting ................................ 182
9.9 Information from Mossbauer Spectroscopy .................. 183
Problem 9 ................................................ 184
Appendix I. The Binomial Theorem and Approximations ........... 187
Appendix II. A Program for Simulating Kirkwood Gap Formation .. 191
Appendix III. A Program for Finding the Orbits of Trojan
Asteroids ................................................ 197
Physical Constants and Useful Data ............................ 205
Solutions to Examples and Problems ............................ 207
Index ......................................................... 239
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