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A pure sine-wave oscillator with a fast settling time

Published online by Cambridge University Press:  01 April 1998

F. N. H. Robinson  and
H. Ockendon
F. N. H. Robinson
Affiliation:
Clarendon Laboratory, Oxford
H. Ockendon
Affiliation:
OCIAM, Mathematical Institute, Oxford
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Abstract

An unforced oscillator which obeys the equation x¨+α (x2+x˙2−1)x˙+x=0 has a pure sine-wave limit cycle which is attained rapidly for a range of values of α. In this paper, free and forced oscillation of this equation are examined experimentally and compared with those for the Van der Pol oscillator. Asymptotic solutions for small α confirm the experimental results.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 9 , Issue 2 , April 1998 , pp. 95 - 104
Copyright
Copyright © Cambridge University Press 1998

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Footnotes

Sadly Dr Robinson died while this paper was being processed. He was a mathematically-minded scientist whose interests far transcended those of EJAM and he will be greatly missed.