Authors: T.C. Lipscombe, C.E. Mungan
The standard harmonic balance method consists in expanding the displacement of an oscillator as a Fourier cosine series in time. A key modification is proposed here, in which the conservative force is additionally expanded as a Fourier sine series in space. As a result, the steady-state oscillation frequency can be expressed in terms of a Bessel series, and the sums of many such series are known or can be developed. The method is illustrated for five different physical situations, including a ball rolling inside a V-shaped ramp, an electron attracted to a charged filament, a large-amplitude pendulum, and a During oscillator. As an example of the results, the predicted period of a simple pendulum swinging between -90° and +90° is found to be only 0.4% larger than the exact value. Even better, the predicted frequency for the V-ramp case turns out to be exact.
Comments: 14 Pages.
Download: PDF
[v1] 2016-01-30 10:22:15
Unique-IP document downloads: 133 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.