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| 研究生： |
洪三原 |
|---|---|
| 論文名稱： |
振動彈簧的擾動性質 On the perturbation of vibrating spring |
| 指導教授： | 李明融 |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用數學系 Department of Mathematical Sciences |
| 論文出版年： | 1998 |
| 畢業學年度： | 86 |
| 語文別： | 英文 |
| 論文頁數： | 41 |
| 外文關鍵詞： | Damping, Life-span, Energy equation, Blow-up, Periodic |
| 相關次數： | 點閱：207 下載：0 |
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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.
Introduction-----1
I Small Free Motions of a Spring-Mass System-----3
I.1 Undamped Motions-----3
I.2 Damped Modons-----6
II The Equation u" = u<sup>3</sup>-----9
II.1 Negative Energy E(0) ＜ 0-----10
II.2 Null Energy E(0) = 0-----18
II.3 Positive Energy E(0) ＞ 0-----23
II.4 The Equation u" = -u<sup>3</sup>-----29
III The Equation u" + ku = εu<sup>3</sup>-----31
Appendix-----36
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