Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- 1 Harmonic Oscillator
- 2 Damped Harmonic Oscillator
- 3 Coupled Oscillators
- 4 The Wave Equation
- 5 Integration
- 6 Waves in Three Dimensions
- 7 Other Wave Equations
- 8 Numerical Methods
- Appendix A Solving ODEs: A Roadmap
- Appendix B Vector Calculus: Curvilinear Coordinates
- References
- Index
3 - Coupled Oscillators
Published online by Cambridge University Press: 02 April 2020
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- 1 Harmonic Oscillator
- 2 Damped Harmonic Oscillator
- 3 Coupled Oscillators
- 4 The Wave Equation
- 5 Integration
- 6 Waves in Three Dimensions
- 7 Other Wave Equations
- 8 Numerical Methods
- Appendix A Solving ODEs: A Roadmap
- Appendix B Vector Calculus: Curvilinear Coordinates
- References
- Index
Summary
We turn next to the case of additional masses.In one dimension, we can attach masses by springs to achieve collective motions that occur at a single frequency, the normal modes.Building general solutions, using superposition, from this ``basis" of solutions is physically relevant and requires a relatively formal treatment of linear algebra, the mathematical topic of the chapter.
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- Mathematical Methods for Oscillations and Waves , pp. 65 - 89Publisher: Cambridge University PressPrint publication year: 2020