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Unformatted text preview: 2 km , the roots are complex (with negative real part), and the solution has oscillations (sine/cosine waves) superimposed on an exponential decay. (f) h(t) and its derivatives has a onemember family of basis functions, { e t } . So we look for a solution of the form Ce t . Substituting this in the differential equation, we find that x t = e t m c k is a solution. ( (m  c + k) = 0 if and only if e t is a homogenous solution.) (g) Laplace transform of each term in the equation yields m s 2 x s m s x m x' c s x s x k x s = a . Putting in the given initial conditions, m s 2 x s c s x s k x s = a or x s = a m s 2 c s k ....
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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.
 Spring '11
 GLAGOLA

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