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ERIC Number: EJ996076
Record Type: Journal
Publication Date: 2012-Sep
Pages: 11
Abstractor: As Provided
ISSN: ISSN-0143-0807
Relativistic Linear Restoring Force
Clark, D.; Franklin, J.; Mann, N.
European Journal of Physics, v33 n5 p1041-1051 Sep 2012
We consider two different forms for a relativistic version of a linear restoring force. The pair comes from taking Hooke's law to be the force appearing on the right-hand side of the relativistic expressions: d"p"/d"t" or d"p"/d["tau"]. Either formulation recovers Hooke's law in the non-relativistic limit. In addition to these two forces, we introduce a form of retardation appropriate for the description of a linear (in displacement) force arising from the interaction of a pair of particles with a relativistic field. The procedure is akin to replacing Coulomb's law in electromagnetism with a retarded form (the first correction in the full relativistic case). This retardation leads to the expected oscillation, but with amplitude growth in both its relativistic and non-relativistic incarnations. (Contains 5 figures and 5 footnotes.)
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: High Schools; Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A