10. Laplace transform and inverse transform a) Take the Laplace transform of the following ODE and find y(s): 4y" + y = (t + 1)²e-2t with initial con- ditions y(0) = -3 and y'(0) = -1. b) Find the inverse Laplace transform of F(s)= 8s+12+ / 4s² + 12s +9+477²*

Q: Compute the Laplace transform. Your answer should be a function of the variable s: s(πt)} = c{₁+ +…

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Q: Q8 Find the Fourier transforms of: sin* - pn Sx< pn f(x) otherwise

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Q: 5- Which of the following is the inverse Laplace transform of the function X (s) = s+ 4s +8 -2t cost…

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Q: Compute the Laplace transform. Your answer should be a function of the variables: L2+ u₂(t)e-³¹…

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Q: Q.1) Find the Laplace transform of the following: a) f (1)=3sin2 21 b) f (1)=3 +° c) f (1)=2cos2t…

A: To solve the following problem we will use the standered result of laplase transformation

Q: 4] Find the Laplace Transform of f(t) = { S-1 (-/= + 5 = /₁1) (1te - 1/₁1) (a) (c) S S - I (b) (d) S…

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Q: 7. Obtain the Fourier sine transform of the following functions: sin wx (c) x² +1' w > 0

A: The given problem is to find the Fourier sine transform of the given function, we have a general…

Q: 1 1 s? +4 s -4 (s+3)

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Q: c) Use a pair (table) to findz-transform of x(n) = 20.65 √2 cos((-)n-1.415)u(n)

A: Introduction: There are many properties that are followed by Z-transformation. It helps us to…

Q: Find the Inverse Laplace Transform of the following: 2. Y(s) = /(2s– 3)5

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Q: Find Laplace transform of the function f(t) = cos(2t + 3)+e¬'u(t – 4) + tcosh²2t

A: Use the following formulas while calculating the Laplace transform of the given function.…

Q: 6. Show that (an)neN C R is bounded if and only if lim supn→∞ an < +∞o.

A: To Prove:  ann is bounded sequence if and only if limsupan&lt;+∞.

Q: 10(2s+5) 6. Find the inverse Laplace transform of I(s) and find s2+3s+2 I(s) when s= 0.1 sec.

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Q: The Laplace transform of x(t) is X(s). Given x(0)=2 and x'(0)=-1, write an expression for the…

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Q: Q3// Find the value of sin лz²+ сos лZ² $c dz (z-1)(z-2) Where C is a rectangular with vertices at…

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Q: Which of the following statement(s) are true? Choose only 2 statements. Lütfen bir ya da daha…

A: The solution is given as

Q: the Fourier transform of a continuous time signal x(t) is X(ja), then, the Fou ansform of the signal…

A: Given, Fourier transform of a continuous-time signal                                   x(t)  ↔…

Q: 2s – 7 - F(s) = %3D (s – 4)(s + 6)

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Q: 6s – 5 Find the Inverse Laplace Transform of F (s) s2+7 5 f (t) = 6cos(/7t). -sin(/77) _cos(/7 ) 5 B…

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Q: Determine the inverse Z-transform of X(z) Select one: akt xk = = (-2j) sin( 2 (2a)k-1 sin (47) 2 xk…

A: Inverse Z transform of the function

Q: 2. ts) Use the table of Laplace Transforms and 1st shifting theorem to find the Laplace transform of…

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Q: The Fourier Transform of * x(t) = [u(t)-u(t-2)][u(t) – u(t − 1)] 8(t - 0.5) cos(2πt) - O exp(j0.5w)…

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Q: (3) A signal has Fourier transform as, 1 sinc (2w X(w) sinc + 2. Compute x(t)

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Q: What is the inverse Laplace transform of 1 /[(s-2) ^2 + 9]? C. 3e^ (-2t) D. 2 sin (2t) 5. A. sin…

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Q: Q5) Find the Fourier transform of: SCos(nt/t) for lel < x(t)=D .elsewhere) Sketch X(f) versus f.On…

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Q: 4.The inverse Laplace transform of { S-3 } is (s-3)2+16

A: ' According to the guidelines iisued by the company we are supposed to answer only one question.…

Q: F(s) = [cots. 14. a sin(22 -t)- sint (b cos(21 – t) – sint di di 2(t1 – 2?) 2(tえ - ) cos (22-t)-…

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Q: Find the Fourier transform of sinc (2t). (a) 2n A(w/2) 3. (b) п Д(u/4) A(w/8 (d) A(w/16) Moving to…

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Q: Find the Inverse Laplace Transform of the following: 1. F(s) (s+5)6

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