Evaluate the given Laplace transform. L(3t² cos(t)} 6(s³ - 3s) a. (s² + 1)² (s³-3s) b. (s² + 1)³ C. 6(5³-5) (s² + 1)³ d. 6(s³ - 3s) (s² + 1)³

Q: L-1{6(s+1)} 54 a. 3t² +t3 b. 3t³+ t² c. 6t² + ³ C. d. 6t³ + t² لاح

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Q: Find the given inverse Laplace transform. 1 € - ¹3 s² +45+5 a. e²¹ sin(t) b. e-2¹ sin(t) C.…

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Q: $² 4. Given F(e-x²) = √e, find the Fourier transform of e-4(x-3)²

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Q: Use Laplace transform to solve the given IVP. = cos 3t, x(0) = 2, ¿(0) = 5 6. * + 9x

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Q: Solve for the following to find the inverse laplace transform.

A: Introduction: Laplace transformation in of the most important integral transformations that…

Q: Use the inverse transforms of some basic functions to find the given inverse transform. x-1,² 9s…

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Q: 6. Find the Inverse Transform of F(s) S-8 3 A f(1) =6+e¬8 – 4e B f(1) =6-e"+ 4e* © s(1) = - 6+ e +…

A: Given- F(s)=6s-1s-8+4s-3 To find the inverse transformation of F(s). Here we will use the following…

Q: -16 LAPLACE TRANSFORMS Find the transform. Show the details of your work. Assume that a, b, w, 0 are…

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Q: -1 [wcose+ssine` s²+w² a. sin (wt + 0) b. sin (t + 0) c. cos (wt + 0) d. cos (t + 0) L-1 }, w & 0…

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Q: 3s+4 -s²+4s+5· a. e2t (3 cost - 2 sint) b.e-2t (3 sint 2 cost) c. e2t (3 sint - 2 cost) d.e-2t (3…

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Q: Find the inverse Laplace Transform of 3(S-1) A. 3(cost + sint) B. (S-1)²+1 3s s²-2s+2 C. 3(S-1)…

A: We will use table of Laplace transform

Q: Evaluate the given Laplace transform. L[3t² cos(t)} a. b. C. d. 6(s³ - 3s) (s² + 1)² (5³-35) (s²+1)³…

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Q: 1. f(t) = e-3t-2| %3D

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Q: L{tcost + sint} 2s a. (s²+1) 2s b. (s²+1)² 25² C. (s²+1)² 25² d. (s²+1)

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Q: The Laplace Transform of cos(√at + 3). s cos 3+ √a sin 3 s²+a a. b. s cos 3-√asin 3 s²+a C. S s²+a +…

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Q: Find all the solutions of cos z = 1+i. Make sure that the solutions you obtained checks out with the…

A: As Many Questions are given , I will solve only first question: We are given cos z=1+i Let…

Q: Q.2 The Laplace Transform a{4e“ – 12cos 2t} is: 4 12s 6s (A) s-6 s' +4 (B) s-6 s+4 4 (C) s-6 s +4…

A: The correct answer is option A. The linearity property of Laplace transform is used here…

Q: 1 The inverse Laplace transform: a{, is: Is²– 36) - (A) 6sin(61 ) (B) -cosh(6t) 1 -sinh(6t) (D) None

A: It is given    Gs=1s2-36=1s2-62         =1·66s2-62=16·6s2-62   The inverse transform is then…

Q: (a) y' + 2y = 26 sin 3t, y(0) = 3. %3D (b) y" + 3y' + 2y = 6e-t, y(0) = 1, y(0) = 2 (c) y" +9y =…

A: Ly''=s2ys-sy0-y'0Ly'=sys-y0

Q: B: The Laplace transform of the; f(t) = e-t.sinh 3t

A: # we are entitled to solve one question at a time , please resubmit the other question if you wish…

Q: 1 £{sin?;nt} 2

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Q: Find the given inverse Laplace transform. 1 € ² [ 3² +65 +10] e-¹. a. e-3tsin(t) b. e³tsin(t) C. d.…

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Q: s2 + 9s + 2 (s – 1)2(s + 3) A. f(t) = et +3tet – 2e-3t C.f(t) = 2e + 3te – e-3t B. f(t) = et + 2tet…

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Q: Use identities plus known transform pairs to find the inverse Fourier transforms of the following…

A: "Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: Give the inverse Laplace transform of -25 + (s – 4) e +9 F(s) = as a function of x. Note: The…

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Q: 3. Evaluate L{4e-2tt3 +t sint cos t}

A: L4e-2tt3+t sint cost

Q: What will be the numerical coefficient of cos(V3t)etin the Inverse Laplace Transform of 3 s(s3-8) O…

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Q: L{12te-³t} 12 a. (s+3) 12 b. (s+3)² 1 C. (s+3)² 12 d.- (s+3)3

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Q: Find the given inverse Laplace transform. e-² [5²2²25) a. −1+e²t b. e²t+2sin(2t) c. 2(1-e-²¹) d.…

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Q: The Inverse Laplace transform of L-¹ 36 [cos (4t 16 81 cos()+4 sin(- 9t cos()-4 sin( 4t cos()-9 sin(…

A: L-1s+916s2+81

Q: a. Determine the formula for the Laplace transform. 4 2 1 L{e³t sin 4t-t² + e¹}= + 3 (s-3)² +16 s³…

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Q: the Laplace t e the ransform of the e functions below. 1. L{2t* – 4t=²} 2. L{cos10t} 3. L{e7t + 7t}…

A: We use properties of Laplace Transform. According to our guidelines only first three questions to be…

Q: 5s + 7 (s + 2)2 A. f(t) = e-2" (5 + 7t) C. f(t) = e-2" (5 – 7t) B. f(t) = e-2"(5 + 3t) D. f(t) =…

A: Use partial fractions and Laplace table.

Q: 4. The inverse Laplace transform L-1{s/(s²+8s +20)}

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Q: Determine the Laplace transform of e-2"cos/3t – t²e-2 3+2

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Q: Which of the following is the inverse Laplace transform of s(s^2 - Use the choices as guide on what…

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Q: 9.) The Inverse Laplace tra (A) In(s² - 2-3 (C) //e+ + 3/e³1

A: Inverse Laplace transform of the function