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A note on small vibrations

Published online by Cambridge University Press:  20 January 2009

Robert Schlapp
Robert Schlapp
Affiliation:
The University, Edinburgh.
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Extract

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This note exhibits some old results in what is possibly a new form.

The simple harmonic oscillator, whose kinetic and potential energies are given in terms of a single coordinate x by

where b is a positive constant, has the equation of motion

The solution, appropriate to the initial conditions at t = 0 is conveniently written

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 7 , Issue 1 , October 1942 , pp. 31 - 38
Copyright
Copyright © Edinburgh Mathematical Society 1942

References

REFERENCES

Turnbull, and Aitkeu, , The Theory of Canonical Matrices (Blackie & Sons, 1931).Google Scholar
Duncan, Fraser, and Collar, , Elementary Matrices (Cambridge Univ. Press, 1938).Google Scholar