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

Q: e-2t cos 3t cOS

A: The given question is related to Laplace Transform. The solution is explained below.

Q: Find Fourier cosine transform of and deduce that - bx -e cos pr di - kog log P+ b? p + a e 1

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Q: Q1. Find the Fourier integral of the given function and discuss it at the discontinuity points 1-x'.…

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Q: Q4 a) 0, if x 0 1,0 < x < 1 x ≥ 1 b) Evaluate Fourier sine transform of f(x) = {¹,0

A: (a) We have to evaluate Fourier integral representation of the given function. f(x)=0if x&lt;012if…

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

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Q: 7. Use the Laplace Transform to solve the IVP y +2y - y -2y= sin(3t) ,y(0) = 0, y'(0) = 0, y'(0) =1

A: We have to use Laplace Transform to solve IVP.

Q: X Q6) Find the Fourier cosine transform of f (x ) = sin x , 0<x <A 0, otherwise

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Q: Solve the equation dy y ху-з dx II +

A: The given equation is of the bernoulli's equation form.

Q: -kx (b) Find the Fourier integral of the function f(x) = e when x > 0 and f(-x) = f(x) for k>0 cos2x…

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Q: (b) Find the Fourier transform of the function given below 1– x? if |x|1 and hence find the value of…

A: Calculate Fourier transform: Fω=∫-∞∞fxe-iωxdx         =∫-111-x2cosωx-isinωxdx…

Q: HW: Find the z transform for sin (ak):

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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: Etample T4 Find the inverse finite cosine transform f (x) if (2nn cos 3 where 0<x < 4. F(n) = (2n +…

A: Inverse finite cosine transform

Q: 53. If Fs (n) is the Fourier sine transform of f (x) on 0<x<1, show that 2nt F.[f" (x)] = [f (0) –…

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Q: 3) Find the Fourier transform of the following signals L. x(t) x(t) + 3 + 2 -2 2 -1 -1 1 -2 using…

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Q: Q2: Find Fourier Transform (FT) of the function f(t) = e-bltl and plot this function in time and…

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Q: What is the first element of z?

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Q: Q.3. Find the fourier expansion for the function whose definition 一T х, (x) = 0, くxく- 2 <x< -

A: Given that function we have to find the Fourier series of that function.

Q: L[sin(3t - 4n)]

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Q: COS TA sin a da 1- cOS Ta sin πα da 4' 2

A: The Fourier sine-transform is the imaginary part of the full Fourier Transform. If f(x) is an odd…

Q: 468 CHAPTER 14 The Fourier Integral end TransforAS sin(x) for -4sx 4 5. S(x)= * for-100 srs100 0 for…

A: In the given question we have to find the fourier integral of the given function f(x) = x2     for…

Q: Q3/ Find Fourier Integral of the function f() = e-klxl , k>0

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Q: (1, |x| 15 Q.1 Find the Fourier transform of f (x) defined by f (x) = %3D Hence evaluate S: sins…

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Q: S1 -x, xl 1 Find the Fourier transform off(x) = and hence evaluate sin x) Cos 2 X COS X – dx.

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Q: (0, 0 b asxsy

A: Fourier Transform

Q: || > 1 {e*cos(x), x|< 1 30. f(x) = {0, %3D Does this function have a Fourier transform (i.e., does…

A: Given fx=excosx, x&lt;1. As it is known that Fourier Transform of fx exists if the function is…

Q: Find the inverse Fourier transform of the function 10 sin(3) w+T

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Q: Find Lf" sin /6t-r'e"}

A: Please see below

Q: 1 Find the Fourier sine and cosine transform of ƒ(x)=

A: Use the Fourier Sine and Cosine transform table to obtain the result.

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

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Q: Use the Fourier transform of cos(k2ot) to find the Fourier transform of a periodic signal x(t) with…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: 1) Find the Fourier Sine transform of the function f(x) = re %3D

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Q: Q6) (a) Prove that Fourier cosine transform of f(x) = cos(x), 1 sin 3(p-1), sin 3(p+1) p-1 p+1 +…

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Q: 7. Find the Fourier sine and cosine transforms of the following functions defined on [0, ∞). x =…

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Q: Σ 4 NITX (пл)з (1- сos(пп)) sin. L f(x) = n=1 8

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Q: (i) Find the Laplace transform of e" sin 21 dt (ii) Form the PDE by eliminating arbitrary constants…

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Q: Q1. Find the Fourier integral of the given function and discuss it at the discontinuity points…

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Q: 4- Find the Fourier sine and cosine transform of: e-x 0 <x < a F(t) = otherwise

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Q: By using Laplace transform to solve y + y = sinht with y (0) = -1, what would the particular…

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Q: [a² - x², Find the Fourier transform of f(x)= • 0, and hence 1C. |x| > a evaluate (Sin sint-t cost…

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Q: x2, Ixl a

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Q: Using Laplace transform, solve y" +y = cos x, where y (0) = 0 = y'(0).

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Q: ve an expression for the x(t) and Determine the Fourier transform of the signal x(t) shown in Figure…

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Q: 4- Find the Fourier sine and cosine transform of: 0 <x < a F(t) = {o otherwise Note: using sin x =…

A: Fourier Sine Transform: Let Fx be defined for x&gt;0. Then Fourier sine transform of Fx is denoted…

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

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Q: >= {1+1) 0 Find the Fourier Integral of f(x) = -π≤x≤π |x|> π

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Q: Solve differential egualions by using laplace transform fCW)-5)'(x)+6f(x)=0 where for-o and flo)=1.

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Q: Q9. (a) i. Find Fourier transform off (x) = x e¯*,0< x < ∞. ii. Find the inverse Fourier sine…

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Q: sin

A: We will compare with the standard expression for Fourier series.