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Unformatted text preview: ME360  Dynamic Systems Prof. Gillespie  Fall 2010 HW 4  Due Sept 30 Problem 1 Problem 2.13, page 70. (Same in the previous book edition). Problem 2 Property No. 3 in Table 3.3.2 on page 104 of your book is a property that I did not derive in lecture. Derive this property. You might start with the derivative property (Property 2 in Table 3.3.2). Problem 3 Problem 3.11, page 151. (Same in the previous book edition). Problem 4 Problem 3.12, page 151. (Same in the previous book edition). Problem 5 Solve each of the following problems using the Laplace Transform method. You solved these same differential equations in the last Homework using the trialsolution method. Also, for each differential equation, check your solution using the Final Value Theorem. That is, evaluate the steady state value both by plugging in t = into the solution and using the Final Value Theorem. a) x + 8 x + 15 x = 30 , x (0) = 10 , x (0) = 4 b) x + 25 x = 100 , x (0) = 10 x (0) = 4 c) x + 8 x + 65 x = 130 x (0) = 10 x (0) = 4 Problem 6 Consider the differential equation x + 2 x + 2 x = 10 , x (0) = 1 , x (0) = 3 . (1) a) Use Laplace transforms to find the solution x ( t ). b) Sketch x ( t ) by hand for t [0 , 5]....
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This note was uploaded on 09/28/2010 for the course MECHENG 360 taught by Professor Gillespie during the Fall '10 term at University of Michigan.
 Fall '10
 Gillespie

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