Book:D.R. Bland/Vibrating Strings

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D.R. Bland: Solutions of Laplace's Equation

Published $1960$, Routledge & Kegan Paul.

Subject Matter


1. Strings of Finite Length
1.1. Introduction
1.2. Derivation of the wave equation
1.3. Solution by separation of variables
1.4. Normal modes
1.5. Examples
1.6. Initial conditions and Fourier sine series
1.7. Kinetic and potential energy
1.8. Examples
1.9. External force and air resistance
2. Travelling Waves
2.1. D'Alembert's solution of the wave equation
2.2. Special cases
2.3. Kinetic and potential energy of travelling waves
2.4. Harmonic waves
2.5. Reflection of waves at a discontinuity of the string
2.6. The effect of air resistance on travelling waves
Answers to Exercises