Find Fourier transform of the Coulomb function -ar e V (r) = 4n r %3D where r = x2 +y2 +z2 . Hint use f (p) = 1 %3D (2 7)3/2 JJJ f(r)e-ip7 d³r

Q: Q2. Find the Fourier transform of the function S2x e- 0<x <1 otherwise f(x) = %3D

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

Q: Find the Laplace Transform of the piecewise function. (2 ,0<t<4; w(t) = { í 1? ,t 4. O 252+e-48…

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Q: Let Rt) be the inverse Laplace transform of 7s2 + 15s – 6 F(s) = (s? + 6s + 10)(s – 2) What is 3/2)?

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Q: Determine the inverse Laplace transform of the function below. 3s2 + 5s + 5 s(s2 + 4s + 5)

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Q: Find the inverse Laplace transform of: 2 s² + 4

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Q: Q1\ Find the Z-transform of A) cosh 2

A: The given question can be solved as shown in step2.

Q: Find the inverse Laplace transform of 6e-1s + le-3s + 3e-5s + 2e¬8s F(s) = . (Use step(t-c) for…

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Q: Find the inverse Laplace transform of F(s)=(7s−6)/(s2−4)

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Q: 10s3+1 1. F(s) %3D s2+6s+5

A: The inverse Laplace transformation transforms a function in s of a complex variable to a real-valued…

Q: Find the inverse Laplace transform of 1 G(s) = s2 – 4s + 5

A: Given,

Q: Find the inverse Laplace Transform of F(s) 2s2 + s -3 F(s) = s4 +3s2 + 2

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Q: Find the Z transform of [cos (ax), x20 f(x)=: 0, x<0

A: Given, fx=cosax,x≥00,x&lt;0 As we know that, Ze-ax=1+e-aτ+e-2τz-2+...=11-e-aτz-1=zz-e-aτ

Q: 3s Find the Inverse Laplace Transform of s2+4s+ 13 (А) -2° ( 3sin3t+2cos3t) B e" (3cos2t – 2sin2t)…

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Q: Find the inverse Laplace transform of [(18s)/((s2+9)2)]e-2s

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Q: Find inverse Laplace transform of the function 7s – 1 F(s) %3D (s + 1)(s + 2)(s - 3) |

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Q: 2s3+ 4s²+1 F(s) = (s²+ 2s+17)(s²+ 4s+20)

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Q: 2s²+7 F(s) (s+1)(s+2)(s²+ 2s+5)

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Q: Find the inverse Laplace transform of F (s) = s+1 s²-6s+5

A: Given function F(s)=s+1s2-6s+5. The objective is to find the inverse Laplace transform of the…

Q: find the inverse Laplace transform of the given function. 3.F(s)=2s2+3s−4F(s)=2s2+3s−4

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Q: Find the inverse Laplace transform of 2e-8s F(s) = s² + 9

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Q: Find the inverse Laplace transform of H(s) -6e-2s s2 – 2s

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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: Find the inverse Laplace transform e-2s L-1 s2 – 4 O 1 zuz sinh(t – 2) sinh2(t – 2) 1 z42 cosh2(t –…

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Q: Find the inverse Laplace transform of F(s) s2 + 2s – 3 . (Use step(t-c) for u.(t) .)

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Q: Q2/ from definition of Fourier transform, show that rect (t-5) is sinc (w/2)e-/2w

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Q: Find the inverse Laplace transform of F(s)=2s+3/(s+1)(s2+9)

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Q: of the function. 4. Find the Fourier transform of of 1/(1+t²).

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Q: 3. Find the Fourier Transform of f(t) = 0, - osts0 le-at, osts ∞ a is positive constant

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Q: Find the inverse Laplace transform e-2s s2 - 4 1 z42sinh2(t – 2) sinh2(t – 2) 1 z42cosh2(1 – 2) 1…

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Q: Find the inverse Laplace transform of L- s-37+4J- 3 (++3)²+4 3 3t e e 3t sin2t sin2t (s+3)2 (C) L"f…

A: Answer

Q: Q2- Find the Fourier Transform for f (t) =A cos o,t, where o, = 2n fo %3D

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Q: .Find the inverse Laplace transform of 3 F(s) s(s? – 2s + s) O-3 – 3t + 3e 03 – 3t + 3e-t 03 + 3t +…

A: F(s)=3s(s2-2s+s)F(s)=3s(s2-s)F(s)=3s2(s-1)Partial…

Q: The inverse Laplace transform of H(s) = + (t) ==²e²+e-²t 8 1 " (3s+2)(S-2) b) f(t) ==e+e-2t -3 d)f…

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Q: Q2:Find the inverse Laplace transform of e-2s F (s) s2 – 2s – 3 - -

A: We have to find the inverse Laplace transform of given function.

Q: Find the inverse Laplace transform of 7s (3s²+75)²

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Q: Q6) A-Show that: a) X(f)=X*(-f) 4 To/2 b) if x(t) is even, then b=0, ano/²x(t) cos(2πnfot) dt…

A: Solution : A) a) X(f)=∫-∞∞x(t)e-jftdt X*(f)=∫-∞∞x(t)e-jftdt* X*(f)=∫-∞∞x*(t)ejftdt…

Q: (a) By making appropriate use of Jordan's lemma, find the Fourier transform of T³ f(x) = (x² + 1)²*

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Q: Find the inverse Laplace transform of F(s)=2s+3/(s+1) (s2+9).

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Q: Find the inverse transform of L-1[ if L-1[f(s)] = F(t) s 2 3/2 4t3/2 4t/2 dt1/2 O O O

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Q: Using Laplace transform method, solve the below initial value y" +25y = 10cos5t, y(0) = 2, y'(0) = 0…

A: To solve the differential equation using the Laplace transform

Q: Find the inverse Laplace transform of: - s-3 i) F(s) = %3D (s-3)2+4 s-2

A: It is known that:

Q: 1.) Give the Fourier transform of the function f. Sx ha x = [0, 1] f(x) = 0 otherwise.

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Q: Find the inverse Laplace transform of 16s3 + 25s2 – 4s + 40 e-78 F(s) s>7. 4s4 + 35s2 – 9

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Q: Find the inverse Laplace transform of the function: 2s3 + 9s² + 11s + 3 F(s) = (s + 1)3 s

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Q: By applying inverse Laplace Transform, we get > y(x) = L-1ſ _2s² + 2 Is²(s² + 5). L={ } - L{4 ++}…

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Q: 1 (iv) If f(t) = e2ºH(t), its Fourier transform is F(@) = -2+iw

A: In this question we have to find whether it is true or false.

Q: Determine the inverse Laplace transform of the function below. 3s2 + 5s + 5 s(s² + 4s + 5)'

A: The given function of s is: 3s2+5s+5ss2+4s+5 Using partial fraction decomposition assume that…

Q: Find the inverse Laplace Transform 2s3 – 9s² + 23s – 10 F (s) = (s² – 4s + 8)²

A: We know that  ℒ-1Fs  is such a function f(t) that  ℒft=Fs. We are given that…

Q: Solve the shifted data initial value problem by the Laplace transform. Show the details. у" — 2y—…

A: Given differential equation,y''-2y'-3y=0,y4= -3,y'(4) = -17

Q: Find the Laplace Transform of f -1 Osx<1 f(x) = 1 x21 2e-s 1 a. 2e-s 52 1 b. 2e-s 1 C. 2e-s 1 d. +

A: We find Laplace transform of given function