Problem 7:) Find the Laplace transform of the functionS(1) = tet + (t – 3)u(t – 1) +e*-©8(t – 2) TABLE OF LAPLACE TRANSFORMSL{1}n!L{t"}sn+1L {sin (at)}s2 + a?L{cos (at)}s2 + a?1S - aL{d(t – a)}L{f(t)8(t – a)}f(a)e-asF(s – a)s"Y (s) – s"-'y(0) – ...- y(n-1)(0)L{f * g}F(s) G(s)-asL{U (t – a)}L{f(t – a)U (t – a)}e-a* F(s)MISCELLANEOUS FORMULASyıf%3DWWY2Yn...W =(n)(n)(n)Yn...

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Answered: Problem 7: ) Find the Laplace transform…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question 5 Find the Laplace transform of 6e5cos2t - et 6(s- 5) A (s – 5)2+4 s- 7 (s - 5) (s - 5)2+4 s+7 6s (c) (s - 5)2+4 s-7 6 D s2+4 s-7 B.
6. Find the inverse Laplace transform of the function I(s) = (3² − a²) (as + b) (s² + a²) (s² + ß²) *
Solve (i) and (ii) using Laplace transform
1. If L{f(t)} = F(s) then L{f""(t)} is, A) s²F(s) sf (0) - f'(0) B) s²F(s)-sf'(0) - f (0) A) B) Statement I only Statement II only 2. Which of the following statements is/are true? I. The Laplace transform of y(V) is s4L(y) - s³y(0) - s²y' (0) - sy" (0) - y'" (0). II. When solved using Laplace transforms, a higher order linear ODE with constant coefficients with available initial conditions yields a general solution. C A) F(s) = B) F(s) = D) -s +3 1 + (s²2s1) s(s² - 2s-1) 1 s(s²2s1) C) D) s³ F(s) - s² f(0) - sf'(0) - f"(0) s³ F(s) - sf'(0) - f (0) 3. What is the Laplace transform of the differential equation and initial value conditions given below? y" - 2y' - y = 1; y(0) = -1; y'(0) = 1 Both statements None of the choices. C) F (s) D) F(s) C) D) = = s+1 (s²2s1) 1 (s²2s-1) 4. Which of the following initial value problem satisfy the given Laplace transform A) y" + y = 0; y(0) = 1; y'(0) = 0 B) y"+y=0; y(0) = 0; y'(0) = 1 + 1 s(s²2s1) L{f(t)} y" + y = 1; y(0) = 0; y'(0) = 0 y" + y = 1;…
If I have a piecewise function that I want to write an f(t) for then take the laplace transform; f(t) = 0 t < 1 e^t-1 1 < t < 2 0 t > 2 How can I sketch this? And how do I find the Laplace transform ? And what does it mean when e is raised to t-1, is this a shift?
Determine the inverse Laplace transform of the given function. Problem h
please solve number 15
Solve for the inverse la place transform of the following functions a) R (s) = b) W (s) c) X(s) = d) y(s) s3-2s²+5s-9 s² (s+3)(s+1) 3s+10 s(s-8)(s-6)² 216 s4+5s3+15s²+45s+54 2S-9 s(s²+10s+146) 16 e)"+ 2y = 48(t – 2π) ; y(0) = 3 and y'(0) = 0 f).y" + 4y = g(x) y(0) = 3 and y'(0) = 0 where g(x) g).y" + 4y' = cos(t - 3) + 4t, y(3) = 0, y'(3) = 7 0 2
Example 2 Find the inverse Laplace transform of 5s + 16 F(s) = (s+2)²(s+5) Bs+C F(s) = (s+a- jw)(s+a+ jw) %3D which has poles at s =-a+ jw and s2 = -a- jw.

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Problem 7: ) Find the Laplace transform of the function S(1) = te" + (t- 3) u(t- 1)+e-8(t - 2)