Derive the Fourier transform for f(t) = te2t for t>0 and 0 for t<0.

Q: f(t) = e cos2t dt

A: Using properties of Laplace transform we solve the given problem as follows :

Q: What is the initial value of f(t) if its Laplace transform is

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Q: Compute the Fourier Transform of f(x) = e-ax-

A: Fourier transform of a function fx is defined as  Ffx=∫-∞∞fxeisx dx Gamma function =∫0∞e-x xn-1 dx

Q: Find the Fourier transform of f(x) without using the Fourier transform table. f(x) = e-l×l. (-0 <x<…

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Q: Compute the Fourier transform of the following function: f(x, y) = e-()x-y|+|x+y\)&

A: The given function is, fx,y=e-x-y+x+y The two dimensional Fourier transform is defined by,…

Q: Use a Fourier transform to solve the following initial value problem for the free Schrödinger…

A: Given: Let us consider the given ut=iuxx ; ux,0=e-x2

Q: Find the Fourier transform of (a) f (x) = sin (x²), (b) f (x) = cos (x2)

A: 4. Given that,fx=sinx2andfx=cosx2The Fourier transform of the above functions isdetermined as shown…

Q: Derive the general formula for the Laplace transform of sin bt.

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Q: dt (te-¹u (t))?

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Q: Find the Fourier transform of -at TE|< 1 fCE) = otherwise

A: We have to solve the given problem.

Q: Use Laplace transform technique to solve , y"-y'-6y= 0, Given y(0) = 1 and y'(0) = -1

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Q: Use the laplace transform to solve 3x'-y=2r;x'+y'-y=0; x(0)=y(0)=0

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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: Use differentiation in time domain to solve the the Laplace transform: y"-y'-6y=0; y(0)=6, y'(0)=13

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Q: f(x) = e-2x sin 5x

A: Given that: find the laplace transform showing complete solution f(x)=e^(-2x) sin 5x

Q: f(t) = 2t + 5et – sin 5t -

A: Given:  ft=2t3+5e4t-sin 5t To Find: The Laplace transform

Q: (1, |t| a

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Q: Determine the Fourier transform of f(t) = te-2t u(t), where

A: Given ft = te-2tut where ut =0     t&lt;01    t&gt;0 The Fourier transformation is given by Fw…

Q: Find the Fourier transform of the Gaussian function f(x) = e-ax".

A: Note "As per our company guidelines we are supposed to answer ?️only first question. please repost…

Q: Compute the Fourier transform of the following function: f (x, y) = e-(1x-y|+|x+y[)<+

A: Calculate Fourier transform: Fu,v=∫y=-∞∞∫x=-∞∞fx,ye-2πjux+vydxdy…

Q: Solve the Laplace Transform of the equation f(t)= te²ᵗsint

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Q: Determine the Fourier transform of e cl, with ca positive number.

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Q: What is the Laplace transform of x(t) = e-tcos(pi)t?

A: To find the Laplace transform of ,  x(t) = e-tcos πt Here the proof for standard form has been…

Q: Obtain the Fourier transform of the function where f(x) = 0 for x &lt; 0 and f(x) = e−axsin(bx) for…

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Q: Find the Fourier transform for x[t] = at*u[t], |a| &lt; 1

A: Given function is,

Q: Determine the Laplace transform of L(t sin 3t)

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Q: Show that x(t) * u(t) x(t)dt %3D and find its Fourier transform.

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Q: Compute the Fourier transform of the following signal: x(t) = e-31e|sin(2t)u(t)

A: The Fourier transform of the function x(t) is represented as X(w), it is defined as ∫-∞∞e-iwtx(t)dt,…

Q: Find the Laplace transform of sinh3 4t

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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 Laplace transform of the function t2 Sint.

A: Find Laplace transform of the function t2 Sint.

Q: Find the Laplace transform of f (t) = sinh3 3t

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Q: Find the Laplace transform of f (x) = 4 sin x + 6 cos 2x

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Q: Find the Fourier transform of f (x) defined bv f x) = , a 10, > a and hence evaluate sin pa cos dp…

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Q: Find the Fourier transform of x(t) shown below using differentiation property * x(t) -1 2)

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Q: 25. а. Apply Fourier transform to solve: ди for 0 < x, t 20 Under the conditions,

A: Given,              ∂u∂t=∂2u∂x2,  for  0≤x, t≥0           (1)Under the conditions,…

Q: Find the Fourier transform for f (x) xe c > 0

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Q: 3. Use a Fourier transform to solve the equation d²y dx2 y 0 with initial conditions y(0) = yo and y…

A: Given: d2ydx2-y2=0 To find: Solving the equation by using Fourier transform.

Q: (a) Find the Fourier Transform of the function: f(t) = e, for t>0 and a > 0.

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Q: Solve the initial value problem using the Laplace transform.

A: Given initial value problem is y'''(t)+5y''(t)+9y'(t)+5y(t)=t2ety(0)=0, y'(0)=0, y''(0)=-2…

Q: Find the Fourier transform of the function : S (t) = e-x2 %3D

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

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Q: Determine the Fourier transform of f if f(x)=e* for x> 0 and f(x)=sinh2x when x< 0.

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Q: i) Find the Fourier sine transform of (sinx, 0 a f(x) %3D 0,

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Q: Find the Laplace transform of the equation. a and b are constant.

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Q: Find the Fourier Transform F(w) = {e-at t≥0 t≤0

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Q: Solve the Laplace Transform 8. f(x) = (2/x)(cos1/2x)

A: note : We will consider the given function as : f(x) = (2/x) cos(0.5x)   Now we have to find the…

Q: Find the Fourier Transform of Seizt -1<t<1 f(t) = = 0 elsewhere

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Q: Find the Fourier Transform of f) = { - z - n<x< 0 0 <x<T

A: We have to find the Fourier Transform of…