Final-f10 - blocks are at rest During the first  à time...

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1 AMS 361: Applied Calculus IV by Prof. Y. Deng Final Test: (12/16/2010) at 2:15PM-4:45PM ESS 001 (1) Open Book and Own Lecture Notes; (2) No Electronics Allowed; (3) Do Any Four of The Five Problems; (4) You Must Mark The Four Problems You Attempt; (5) Will Only Grade The First Four If You Don’t Mark; (6) Each Problem Is Worth 9.0 Points As Indicated with Max 35 Points; (7) Covers Material for the Full Semester; (7) No Name, No Grades. Class ID: Name: You must write your name here. No Name, No Score! SBID: Problems To Grade? Score Remarks F-1 F-2 F-3 F-4 F-5 Total Score F-1 (9.0 Points): Find the general solution of the following DE ± ² ³ ´µ ¶ ·¸ ¹ ± ¶ º± »¼ ± ½ ¾ where ¿ is a large given integer, for example, ¿ ½ º¾·¾ . F-2 (9.0 Points): Two blocks of masses À and Á are attached to three mass-less springs of the same spring constant. They are placed on a horizontal and perfectly smooth bench. Initially, the blocks are placed with spring staying at their natural lengths and both
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Unformatted text preview: blocks are at rest. During the first  à time, a constant force Ä is added to the left block Å from left to right. At the end of the  à time, immediately, a constant force “ ³Ä ” (same magnitude and at the opposite direction) is added to the same block for ÂÆà time. Then, no more external force is added to the blocks. Find the displacements of the blocks as a function of time. M m 2 F-3 (9.0 Points): Solve the following equations ± ²² ³ ´± ² ³ ± µ ¶·¸ ¹ º» ³ ¼·¸ ¹ ½» ±·¾» µ ¾ ± ² ·¾» µ ¾ ¿ where À and Á are given constants. F-4 (9.0 Points): Solve the following integral equation: ±·¸» µ ¸Ã ÄÅ ¹ Æ Ã Ç·ÅÈÉ» ±· Å Ê Ë»ÌË F-5 (9.0 Points): Find the general solutions of the following system of equations using any one of your favorite methods: ± ² ¹ ± ¹ ´Í ¹ Î µ ¾ Í ² ¹ ϱ ³ Í µ ¾ Î ² ³ ± ³ ´Í ³ Î µ ¾ ¿...
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Final-f10 - blocks are at rest During the first  à time...

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