카이스트 고전역학 기말 족보.docx
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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 consistin…(생략(省略))
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카이스트 고전역학 기말 족보.docx
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카이스트 고전역학 기말 족보.docx
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