6. please show all work and circle answer
6. please show all work and circle answer ① Using Laplace transform to solle lup yaby-...
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Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let be a function defined for t 2 0. Then the integral LARE)) = -stPct) of Find is said to be the Laplace transform of provided that the integral converges. ). (Write your answer as a function of s.) (t) =35, Ost2 Lot 2 2 CZA()= 2 9e-25 (s > 0)
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(1 point) Use Laplace transforms to solve the integral equation y(t) – v yết – U) do = 4. The first step is to apply the Laplace transform and solve for Y(s) = L(y(t)) Y(s) = Next apply the inverse Laplace transform to obtain y(t) y(t) =
Use the Laplace transform table and the linearity of the Laplace transform to determine the following transform. Complete parts a and b below. £{e 9t sin 8t - +++ et} Click the icon to view the Laplace transform table a. Determine the formula for the Laplace transform. 2{e et sin 8t - +4 + t) =(Type an expression using s as the variable.) b. What is the restriction on s? (Type an integer or a fraction.) S>
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(1 point) Find the Laplace transform F(s) of f(t) = e4-24u(t - 6) F(8) =
Question (2): Laplace Transformsa) Find the Laplace Transform of the following using the Laplace Transform table provided in the back:$$ f(t)=\frac{1}{4}\left(3 e^{-2 t}-8 e^{-4 t}+9 e^{-6 t}\right) u(t) $$b) Find the inverse Laplace Transform \(F(s)\) of the following function \(f(t)\) using the table:$$ f(t)=\frac{12 s^{2}(s+1)}{\left(8 s^{2}+5 s+800\right)(s+5)^{2}(10 s+8)} $$
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1. Solve the following Laplace Transform problems: (a) (20 points) Given the following function f(t) = [10+ (4e-2+ + 3te-4t)e2t]u(t) A Find F(s) = C[f(t) as a proper rational function. F(8) must be in fully factored form. (b) (20 points) Let: f(t) = Ś(n + 2)!e=n(+36)(t – 3n) Find F(s) = [f(t) as a proper rational function.
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The Laplace transform of the piece wise continuous o<t<3 is given by: a) None of them 6) L {f} = = (2-e-st), S70 c)L{f} = 2 (3-e-st), s so dX[f) = 4 (1-2 est), so e) L {f} = } Show your complete wone. = ₃ (1-3e-st), 530
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(1 point) Find the Laplace transform F(s) of f(t) { O, t<6 5 sin(at), 6<t<7 0, t> 7 F(8)
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steps.
(1 point) Use the Laplace transform to solve the following initial value problem: x' = 5x + 3y, y = -2x +36 x(0) = 0, y0) = 0 Let X(s) = L{x(t)}, and Ys) = L{y(t)}. Find the expressions you obtain by taking the Laplace transform of both differential equations and solving for YS) and X (s): X(S) = Y(s) = Find the partial fraction decomposition of X(s) and...
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(1 point) Use the Laplace transform to solve the following initial value problem: y6y9y 0,with y(0) 1, y (0) = -4 First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)} find the equation you get by taking the Laplace transform of the differential equation =0 Now solve for Y(s) = and write the above answer in its partial fraction decomposition, A Y(s) (s+a} s+a Y(s) Now by inverting the transform,...