Find the inverse Laplace of Find the solution of the DE using Laplace Transform y" - 4y +4y=cos(t); y(0) = 1, y(0)=-1 (1+e-²π(s+1))(s+1) s²+2s+2

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

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Q: Show that the Fourier transform of f (x)= e*/2 is e

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Q: Find the Laplace transform of the equation: y′′−4y=sin2t when y(0)=0, y′(0)=2 choices: a.)…

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Q: find the Fourier transform f(x) = e ¹² cos fx|

A: What is Fourier Transformation: A mathematical transformation known as the Fourier transform…

Q: Use Laplace transform technique to solve y +2y +2y= e-, y(0) = - 4, y'(0) = - 2

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Q: f(t)=u(t-3)(t-3)e-4t Obtain the Fourier transform of the function

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Q: SOLVE FOR LAPLACE TRANSFORM e" (cost + 3 sin t) e-3 -2t e2t (t3 + 5t – 2) sin 2t sin 5t

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Q: Find the Laplace transform of f(t) = sin² 5t a. 50/($³+125s) 25/(s³+ 100s) b. C. 25/(s³ + 125s) d.…

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Q: The Fourier transform of the function f(t) = 2e-2t cosh 2t u(t)is: 2 4 A- πδ (ω) B- πδ(ω )+ j2w+w?’…

A: We have to use formula for Fourier Transform.

Q: Solve the shifted data IVP by the Laplace transform method showing your work in details.…

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Q: • Let: X₁ (jw) = 2nd(w) + nd(w − 4ñ) + ñ8(w + 4π) • Use the inverse Fourier Transform to find x₁(t)…

A: Introduction: Like other integral transformation, Fourier transformation has also its inverse. In…

Q: Determine the Laplace transform of the equation f (x) = 2e-"sin4t 16 A s2+ 4s + 20 20 B s2+ 4s + 20…

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Q: 2) find the fourier transform x(t) = u(t) x(t) ulzt) x²(t) = u(+ + 5) -

A: xt=utxt=u2txt=ut+5xt=ute-jw0t

Q: -2sin4t Determine the Laplace transform of the equation f (x) = 2 e´ 10 A s²+4s+20 8 B s²+4s+ 20 20…

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Q: -Obtain the Fourier transform of f(t): = sin (30) -t²+7it+12

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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: Use Laplace transform technique to solve y+2y+2y=e, y(0) = 3, y (0)=-3

A: We need to use Laplace transform to solve this differential equation.

Q: Find the Fourier transform specified in part (a) and then use it to answer part (b). (a) Find the…

A: In part (a) we have to find the Fourier transformation, Given, f(γ,p,t)=e-γtsin pt  t>0,0…

Q: dx + 2xy = sin y , x(n) = 1 - dy

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Q: Find the Fourier Transform of f(s) = e-ax= a >0

A: The Fourier transform of a function  is given by :

Q: a Find the Fourier transform of the signal x(7) = 2 cos(m)[(1+3)-(1-3)], using the Fourier integral.

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Q: Use Laplace transform technique to solve y + y"+2y +2y e, y(0) = - 3, y (0) = 2 %3D

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Q: Find the Fourier transform F(@) = | f(t)exp(iwt)dt of the function 0, t 0. You might want to use…

A: The given function is ft=0t<01βtt≥0, where β>0. We know that the Fourier transform of a…

Q: Find the fourier transform of f(t) = e-2(t+4)ʻ sin (nt).

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Q: Find the fourier trans y (t) = x (+). Cos wot

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