b) Find the Laplace transform, inverse Laplace, and ODE solution by Laplace method of the following functions (choose FOUR only). 1) f(s) = 2) f(t) = cos(4t) (e³t + 5)² 3 $-5 8(s+1) (s-5)2+15 4) y - 2y + 5y + 8 e* = 0, y(0) = 2, y (0) = 12 + 5) f(s) = 3) f(t) = s+2 S³+952+24s+16

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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

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Q: 2C

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A: Inverse Laplace Transform: Definition: If Fs be the Laplace transform of a function ft, that is if…

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Q: Find the Laplace Transform of the following functions: F(8)= F(s) = = F(s) = f(t) = 6e -6t +91² + 5t…

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Q: . Find the Laplace transform of the function f(t) = 2t + 3 cos(3t) + 4 sin(3t)

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Q: 2. (a) Show that gi(t)g2(t) G₁(f) * G₂(f) where denotes convolution and gi(t) = G₁(f), 92(t)=G₂(f).…

A: We start with the time-domain signals and their Fourier transforms:Now, the convolution in the time…

Q: B) Find Laplace transform of each of the following: 1) f(x) = 0.5e3x + cos(bx) ex sin(cx) - at 25 2)…

A: Solution of the given question is like as

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Q: Q1: Find inverse Laplace transform of the following functions 3s s²+2S-8 4) F (s) = 5) F(s): = S+12…

A: The given problem is to find the inverse Laplace transforms of the given functions.

Q: 2. Determine the Laplace transform of the given function a) f(t) = e³¹t4 b) f(t

A: Laplace transform

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A: We have to solve the problem

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Q: 2. Determine the Laplace transform of the given function. a) f(t) = e³¹t4 c) f(t) = est sin(3t) e)…

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Q: Compute eigenvalues and eigenvectors for the matrix: GJ O λι = ί λ = - 31 = A₁ = 1 A₂ = -1 --0--0 =…

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Q: Exercise (2): Find the inverse Laplace transform of the following functions. 59}. (1) L- (2) L-1 (3)…

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Q: The question involves finding the inverse Fourier Transform of the following functions:

A: see the attachment given below for details.Explanation: