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Unformatted text preview: evaluating the following equation: lim 1/ Â° 1+ Â± 1 âˆ’Â± 2 Â²Â³ + y dt = lim Â´ÂµÂ¶ âˆ’ 1 Â· Â¸Â¶ 1+ Â± 1 âˆ’Â± Ïµ â†’ 0 Ïµ â†’ 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 Â¹ Â³ + 2 Â¹ Âº + 5I = Â» Âº a, I(0) = I , Â¹ Âº (0) = Â¹ Âº Â¹ Âº = V a (0) âˆ’ ( 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 âˆ’t sin 2t)/2 (c) Write the solution to (1) for arbitrary forcing. 10. Page 502, number 16...
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 Fall '08
 Edwards,D
 Differential Equations, Linear Algebra, Algebra, Equations, Laplace, following equation

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