Lab 6 - evaluating the following equation: lim 1/ ° 1+ ±...

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MATH 342-010 Differential Equations with Linear Algebra II Fall 2009 Due October 16, 2009 Homework 6 Edwards and Penney Section 7.4 1. Page 481, numbers 17 and 20 Section 7.5 2. Page 491, number 22 3. (a) Find the Laplace transform of (t − 1) 2 u 2 (t). (b) Find the inverse Laplace transform of e -s (s + 6)/(s 2 +9) 4. Find the solution of ° + 3 °± + 2 ° = 1 – u 1 (t) ° (0) = 1, °± (0) = 1. 5. Page 492, number 30 6. Page 492, number 40 Section 7.6 7. Page 502, numbers 2 and 8 8. Consider the following equation: (1/a 2 ) ² + y = δ (t − 1), y(0) = 0, ²± (0) = 1.
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(a) Using Laplace transforms, show that the solution is given by y(t) =sin at/a + au 1 (t) sin a(t − 1). (b) Calculate the magnitude of the jump in the derivative at t = 1 by direct calculation. (c) Calculate the magnitude of the jump in the derivative by
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Unformatted text preview: evaluating the following equation: lim 1/ ° 1+ ± 1 −± 2 ²³ + y dt = lim ´µ¶ − 1 · ¸¶ 1+ ± 1 −± ϵ → 0 ϵ → 0 9. Consider the series RLC circuit shown in the figure to which an arbitrary voltage V a (t) is applied. There is an initial voltage on the capacitor of V c and initially there is a current I in the inductor. The governing equations for this system are ¹ ³ + 2 ¹ º + 5I = » º a, I(0) = I , ¹ º (0) = ¹ º ¹ º = V a (0) − ( V C + 2 I ). (1) (a) Using Laplace transforms, calculate the solution to (1) in the case of no forcing. (b) Show that the impulse response g(t) for this problem is given by g(t) =(e −t sin 2t)/2 (c) Write the solution to (1) for arbitrary forcing. 10. Page 502, number 16...
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This note was uploaded on 12/23/2009 for the course MATH 342 taught by Professor Edwards,d during the Fall '08 term at University of Delaware.

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Lab 6 - evaluating the following equation: lim 1/ ° 1+ ±...

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