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test4prf3-f8-1

# test4prf3-f8-1 - MATH 2403F3-F8 Practice Problems for...

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MATH 2403F3-F8 Practice Problems for Midterm 4 Fall 2009 TIME: November 17 (Tuesday), 12:05-13:05 (the length of the exam is 60 min) PLACE: Howey Physics L1 (where we meet on Tuesdays & Thursdays) COVERAGE: Lectures 10/22-11/10 EXAM POLICY: No calculator. No books. No notes, except for one formula sheet of letter size handwritten by yourself. Turn in this formula sheet with your test. By the way, a copy of Table 5.3.1 on page 325 will be provided to you at this test. The problems below are only meant for your practice. The real problems on the exam will not be the same. The amount of questions will also not be the same. Good luck! [1] Find the inverse Laplace transform of G ( s ) = - 5 s + 3 s 6 + 1 ( s - 5) 3 + - 4 s 2 - 5 s + 14 ( s - 2)( s - 4)( s + 1) + 2 s + 1 s 2 + π 2 - 3 s ( s - 3) 2 + π 2 . [2] Use the Laplace transform to find the solution of the following initial value problems: (a) y + 2 y + y = 8 e 3 t , y (0) = 0 , y (0) = 1 . (b) x = - 6 x + 4 y, y = 5 x, x (0) = 6 , x (0) = - 6 , y (0) = 6 . [3] (a) Find the Laplace transform of f ( t ) = t 2 t < 3, 2 t - 8 3 t < 5, 2 5 t < 6, 1 t

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test4prf3-f8-1 - MATH 2403F3-F8 Practice Problems for...

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