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Linear Fractionally Damped Oscillator
Author
Source
International Journal of Differential Equations
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-10-22
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
The linearly damped oscillator equation is considered with the damping term generalized to a Caputo fractional derivative.
The order of the derivative being considered is 0≤v≤1.
At the lower end (v=0) the equation represents an undamped oscillator and at the upper end (v=1) the ordinary linearly damped oscillator equation is recovered.
A solution is found analytically, and a comparison with the ordinary linearly damped oscillator is made.
It is found that there are nine distinct cases as opposed to the usual three for the ordinary equation (damped, over-damped, and critically damped).
For three of these cases it is shown that the frequency of oscillation actually increases with increasing damping order before eventually falling to the limiting value given by the ordinary damped oscillator equation.
For the other six cases the behavior is as expected, the frequency of oscillation decreases with increasing order of the derivative (damping term).
American Psychological Association (APA)
Naber, Mark. 2009. Linear Fractionally Damped Oscillator. International Journal of Differential Equations،Vol. 2010, no. 2010, pp.1-12.
https://search.emarefa.net/detail/BIM-453754
Modern Language Association (MLA)
Naber, Mark. Linear Fractionally Damped Oscillator. International Journal of Differential Equations No. 2010 (2010), pp.1-12.
https://search.emarefa.net/detail/BIM-453754
American Medical Association (AMA)
Naber, Mark. Linear Fractionally Damped Oscillator. International Journal of Differential Equations. 2009. Vol. 2010, no. 2010, pp.1-12.
https://search.emarefa.net/detail/BIM-453754
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-453754