Abstract
In the early part of the 18th century the eigenfrequencies of the transverse vibrations of a string were determined by Brook Taylor, Jean d Alembert, Leonhard Euler, and Daniel Bernoulli: the circular frequencies are
with L being the length and μ the mass per unit length of the string and F the tensile force; the odd integers n =1, 3, 5, ... correspond to the symmetric, the even integers n =2, 4, 6, ... to the antisymmetric vibration modes. This formula can be derived simply by application of Newton’s law on the strain forces and the mass of the string element.
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References
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© 1987 Birkhäuser Verlag Basel
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Laasonen, P. (1987). The Hybrid Dissolution of a Double Eigenvalue. In: Albrecht, J., Collatz, L., Velte, W., Wunderlich, W. (eds) Numerical Treatment of Eigenvalue Problems Vol.4 / Numerische Behandlung von Eigenwertaufgaben Band 4. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik Série internationale d’Analyse numérique, vol 83. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7507-3_12
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DOI: https://doi.org/10.1007/978-3-0348-7507-3_12
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