The spring‐mass system revisited
作者:
James T. Cushing,
期刊:
American Journal of Physics
(AIP Available online 1984)
卷期:
Volume 52,
issue 10
页码: 925-933
ISSN:0002-9505
年代: 1984
DOI:10.1119/1.13796
出版商: American Association of Physics Teachers
关键词: SPRINGS;OSCILLATIONS;BOUNDARY CONDITIONS;EQUATIONS OF MOTION
数据来源: AIP
摘要:
A vertically oscillating spring of massmand spring constantksuspended from its upper end and with a massMattached to its lower end is a system often used for demonstrations and experiments in introductory physics courses. We discuss the motion of this system for arbitrary values of ε=m/M, 0≤ε<∞ and show explicitly why theory predicts that the amplitude of the lowest normal‐mode frequency makes the major contribution to the motion ofM(or of the lower end of the spring) forallvalues of ε. Although a complete understanding of this fact involves detailed mathematical analysis, the results themselves are simply stated and readily verified even by students in an introductory calculus‐based physics course. The various predictions of the theory are easily demonstrated with simple equipment and lend themselves nicely to an introductory physics laboratory. These applications are discussed in some detail, and an analog electric circuit is given which exhibits similar behavior.
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