카이스트 고전역학 기말 족보.docx

2015 Classical Mechanics I Final-term Exam 2015. 6. 19 20:00 ~ 1. (To be scored by Prof.) 2. (a) Show that the superposition principle does not hold for a nonlinear differential equation such as . Here is a constant. (4 points) Let and are possible solutions of the differential equation. If we apply a trial superposition solution to the equation, then . Therefore, the superposition principle does not hold for such a nonlinear differential equation. (b) Consider the system represented as Here, is a small, positive constant. Show that the system has a simple limit cycle, and describe the motions of the variables with brief sketches. (6 points) Change the variables as and . Then . In similar, . Let , then . Finally, where , For large , in which , and . Thus this system has a simple limit cycle with and . Or and , and and . (4 points) A brief sketch can be drawn as (2 points) 3. Consider an isolated two-particle system consisting of and . Gr…
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