Cover -- Half Title page -- Title page -- Copyright page -- Dedication -- Preface -- Chapter 1: Classical Perspective -- 1.1 Importance of the Harmonic Oscillator -- 1.2 Newtonian Perspective -- 1.3 Restoring Force -- 1.4 Free Harmonic Oscillator -- 1.5 LC Resonator -- 1.6 Journey Through the Center of the Earth -- 1.7 Low Satellite Orbit -- 1.8 FREE-OSC, Free Oscillator Worksheet -- 1.9 Phase Space, Part 1 -- 1.10 PHASE-SP, Phase Space Worksheet -- 1.11 Callisto, Galileo, and French -- 1.12 Searching for Planets -- 1.13 Franklin, Priestly, Verne, and Burroughs -- What's Next? -- Chapter 2: Oscillator Energy -- 2.1 Conservative Forces -- 2.2 Potential Energy -- 2.3 Kinetic Energy -- 2.4 Conservation of Energy -- 2.5 Phase Space, Part 2 -- 2.6 Energy Diagrams -- 2.7 Equipartition of Energy -- 2.8 General Potential Energy Function -- 2.9 Perturbed Satellite Orbit -- 2.10 High Power-Law Oscillators -- 2.11 Adiabatic Invariance -- 2.12 UNDAMPED, Free Oscillator Energy Worksheet -- 2.13 Bungee Jumpers Beware -- 2.14 Summary -- Chapter 3: Damped Oscillators -- 3.1 Velocity-Dependent Resistive Force -- 3.2 FORCE-RV, Resistive Force Worksheet -- 3.3 Restoring Force and Resistive Force -- 3.4 Under-Damped Oscillator -- 3.5 Critically Damped Oscillator -- 3.6 Over-Damped Oscillator -- 3.7 Summary of Free, Damped Oscillators -- What's Next? -- Chapter 4: Forced Oscillators -- 4.1 Forced Free Mass -- 4.2 Forced Damped Mass -- 4.3 General Solution for Forced Damped Mass -- 4.4 Power Transfer -- 4.5 Forced Damped Oscillator -- 4.6 Permittivity for Bound Charges -- 4.7 FORCEOSC, Forced Oscillator Worksheet -- 4.8 Summary -- What's Next? -- Chapter 5: Q, R, X, Y, and Z -- 5.1 What Is Q? -- 5.2 Frequency Domain -- 5.3 Time Domain -- 5.4 Q of Various Oscillators -- 5.6 Resonant Detection, Mössbauer Effect -- 5.7 Q Multipliers and Dividers -- 5.8 Q Switches.

5.9 Classical Uncertainty Principle, Part 1 -- 5.10 ABC-OF-Q, Worksheet in Time and Frequency -- 5.11 Impedance and Admittance -- 5.12 Impedance and Admittance: Damped Mass -- 5.13 Impedance and Admittance: Harmonic Oscillator -- 5.14 Y-AND-Z, Admittance and Impedance Worksheet -- 5.15 How Henry Cavendish Weighed Planet Earth -- What's Next? -- Chapter 6: Fourier Perspective -- 6.1 Signal Classification -- 6.2 Periodic Signals -- 6.3 Oscillator with Periodic Force -- 6.4 Bandwidth and Spectral Density -- 6.5 Laplace's Equation -- 6.6 Non-Periodic Signals -- 6.7 Classical Uncertainty Principle, Part 2 -- 6.8 Alternative Formats -- 6.9 Laplace Transform -- 6.10 Hilbert Transform -- 6.11 Parseval's Theorem -- 6.12 Joint Time-Frequency Analysis -- 6.13 Inductive Leap -- What's Next? -- Chapter 7: Elements of Linear Systems -- 7.1 What Is a Linear System? -- 7.2 Ode to the Sinusoid -- 7.3 Fast Fourier Transform -- 7.4 Test Signals -- 7.5 Step Function Response -- 7.6 Impulse Response -- 7.7 Frequency Domain Response Using Phasors -- 7.8 Impulse Response and Causality -- 7.9 System Function via Fourier Transform -- 7.10 Impulse Response via Fourier Transform -- 7.11 Convolution -- 7.12 Power Spectral Density -- 7.13 Wiener-Khintchine Theorem -- 7.14 Auto- and Cross-Correlation Functions -- 7.15 Coherence Function -- 7.16 System Identification -- 7.17 Deconvolution -- 7.18 Data Windows -- 7.19 Central Limit Theorem -- What's Next? -- Chapter 8: Methods of Advanced Dynamics -- 8.1 Generalized Coordinates -- 8.2 Generalized Momenta -- 8.3 Lagrange's Equations -- 8.4 Hamilton's Equations -- 8.5 Poisson Brackets -- 8.6 Hamilton's Principle -- 8.7 Hamilton-Jacobi Equation -- 8.8 Symmetry of the Hamiltonian Function -- What's Next? -- Chapter 9: Coupled Oscillators -- 9.1 Two Coupled Oscillators -- 9.2 Magnetically Coupled Resonators.

9.3 COUPLOSC, Worksheet for Coupled Oscillators -- 9.4 Time Evolution, Weak Coupling -- 9.5 COUPLOS2, Worksheet #2 for Coupled Oscillators -- 9.6 Normal Coordinates -- 9.7 Oscillating Galaxies -- 9.8 Synchronized Oscillators -- What's Next? -- Chapter 10: Statistical Perspective -- 10.1 Distributions and Moments -- 10.2 Accuracy and Precision -- 10.3 Parable of the Bunny Rabbits -- 10.4 Displacement Probability Density -- 10.5 Uncertainty Due to Thermal Motion -- 10.6 More Distribution Functions -- 10.7 Natural Sources of Randomness -- 10.8 Poisson, Exponential, and Gaussian Distributions -- 10.9 Random Excitation -- 10.10 Entropy -- 10.11 Virial Theorem -- 10.12 Liouville's Theorem -- 10.13 Information and Noise -- 10.14 Stochastic Resonance -- 10.15 Phase Space Correlation and Covariance -- 10.16 Predictability -- 10.17 Time Evolution and Predictions -- 10.18 Expectation Values: Caveat Emptor -- 10.19 Expert Opinions on Predictability and Causality -- What's Next? -- Chapter 11: Quantum Perspective -- 11.1 Classical Crisis -- 11.2 A Collection of Oscillators -- 11.3 PLANCK, Worksheet for Blackbody Radiation -- 11.4 Harmonic Oscillators and Radiation -- 11.5 Wilson-Sommerfeld-Ishiwara Quantization Rule -- 11.6 Summary of Energy Level Spacing -- 11.7 Quantization of Angular Momentum -- What's Next? -- Chapter 12: Quantum Oscillators -- 12.1 Wave-Like Property of Momentum -- 12.2 Schrödinger Equation -- 12.3 Dynamic Variables and Their Operators -- 12.4 Free Particle -- 12.5 A Particle in a Box -- 12.6 Superposition of States -- 12.7 Electric Dipole Radiation -- 12.8 Dipole Transitions, Particle in a Box -- 12.10 Harmonic Oscillator -- 12.11 Harmonic Oscillator Dipole Transitions -- 12.12 QUANTOSC, Quantum Oscillator Worksheet -- 12.13 Revival of Wavefunctions -- 12.14 Discovery of Classical Oscillators -- 12.15 Meanwhile, Back in Heligoland ….

12.16 Single-Electron Oscillator -- 12.17 Trouble in Paradise -- What's Next? -- Appendix 1: Worksheets -- Installing the Files from the Diskette -- Useful Spreadsheet Functions -- Appendix 2: The Hilbert Transform -- A2.1 Derivation via Unit Step -- A2.2 Constructing an Analytic Function -- A2.3 Fourier Transform of Unit Step -- A2.4 Application of the Hilbert Transform -- A2.6 References for the Hilbert Transform -- Bibliography -- Books -- Software -- Selected Papers from American Journal of Physics -- Selected Papers from Other Journals -- Index.