Exam1 - m(f If h t = e − t find a solution x(t Assume that e − t is not a homogenous solution(g Find the Laplace transform of the differential

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Engineering Analysis Exam 1 Balance of forces for a damped linear oscillator gives m d 2 x dt 2 =− c dx dt kx h t where c , k , m are positive numbers. (a) Write this differential equation in standard form. (b) Classify this differential equation. Be as specific as possible. (c) Find the general solution for the case h(t) = 0 . (d) If h(t) = 0 , x(0) = b , and x'(0) = 0 , find the particular solution x(t) . (e) For this particular solution, distinguish three regimes in the behavior of x(t) at positive t , depending on the relative values of c , k , and
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Unformatted text preview: m . (f) If h t = e − t , find a solution x(t) . Assume that e − t is not a homogenous solution. (g) Find the Laplace transform of the differential equation if h(t) = aδ(t) , x(0) = 0 , and x'(0) = 0 . ( δ(t) stands for the Dirac delta function.) Solve for x s . Possibly useful formulas: Quadratic formula: x = − b ± b 2 − 4 a c 2 a Integration by parts: ∫ a b f x g' x dx = f x g x ] a b − ∫ a b f ' x g x dx...
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This note was uploaded on 08/30/2011 for the course CGN 2200 taught by Professor Glagola during the Spring '11 term at University of Florida.

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