In this work we deal with the nonlinear o.d.e u"+ku = εu<sup>3</sup> which represents a spring-mass system with no damping but perturbed by external force εu<sup>3</sup>. We want to know how the spring constant k and the perturbed term act on the equation. So we study this equation by the way:
(I) u" + ku = 0 (II)u" = u<sup>3</sup> (III) u" + ku = εu<sup>3</sup>
During the period of calculating, we find that k, ε and energy constant E(0) play important roles in the properties of the solutions of the equation. Finally we give the relation about them.
| Identifer | oai:union.ndltd.org:CHENGCHI/B2002002161 |
| Creators | 洪三原 |
| Publisher | 國立政治大學 |
| Source Sets | National Chengchi University Libraries |
| Language | 英文 |
| Detected Language | English |
| Type | text |
| Rights | Copyright © nccu library on behalf of the copyright holders |
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