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# HW4 - ME360 Dynamic Systems Prof Gillespie Fall 2010 HW 4...

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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 trial-solution 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]. c) Build a Simulink block diagram to simulate this system, and turn in a printout of your Simulink block diagram and the output x ( t ) for t [0 , 5].

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