3. Solving the following problem using Fourier transformation method. du d²u a² -= 0, (t> 0, -∞0 < x <∞) Ət əx² u(x,0) = sin x -

Q: f (t) ) — е -4(t-2)² e

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Q: How to solve this equation y''' - 8y" + 4y' +48= 4x2+1 using Laplace Transformation.

A: Converting the equation in Laplace transform:…

Q: In the case where a = -T and b = T, compute (sin px, sin qx), (sin px, cos qx), and (cos px, cos…

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Q: Calculate the Fourier Transforms of the following functions: 1, |x| 1

A: According to guidelines we  have to solve the  first  one question.

Q: as Calculate (x sin y + e). ax²əy³

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Q: Let f(x) (x2 +x), -n<x<n be a periodic function, then the Fourier coefficient az %3D Answer:

A: The Fourier series for the function can be calculated using the formula  fx=A0+∑n=1∞…

Q: then prove that i) F, [ƒ (x) cos ax] = [f, (p + a) +f, (p a)] 1 ii) F.[f(x) sin ax] 2 [f. (p + a) –…

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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: Q: The Fourier representation of a function f(x): f(x) = {-10 V, 10 V, ーTくX x > 0 40 sinx sin3x…

A: Given f(x) = -10v.  When -π &lt; x &lt; 0              = 10v when 0 &lt; x &lt; π.   Graph of this…

Q: x2 , Ix1 a = find Fourier transform of f(x)=

A: To determine: The Fourier transformation of  f(x) = x2 ,     x&lt;a 0 ,       x&gt;a

Q: Find the Fourier coefficients of the periodic function f(x)=x-2x², (-<x<n); f(x+2) = f(x)

A: We have to solve by Fourier series.

Q: - 34 as f(4)= ė" ult-1) Solve it in fourier transformation

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Q: Find the Fourier transform of each function. In each case, a is a positive real constant. Answer:…

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Q: Find the complex transform of F(x) = e¬l\l, –∞ < x < ∞

A: Complex Fourier Transform or Fourier Transform: Let Fx be a function defined on R Then Complex…

Q: O [-5, -1) U (1,6] O (-5,6] O [-5, 6] O (-5, -1] U [1, 6] Find the domain of r(t) = (ln(t + 5),…

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Q: 235 óf the textbc (d) F{e* ,5iz-az²

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Q: Laplace transform a. L- (¹) 48 b. L-¹ { 1/2-) S5 C. 1 L-1 (2435) s²+3s. :-1 (432 +1} d. L-1

A: We have used standard formulae of Laplace transform.

Q: 2.) у" - Зу' — 2у %3D0 У (0) %3D0, у'(0) %3D 9 ,у" %3D0

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Q: Find the Fourier integral representation of the function, "a²-x² if 0a f(x) =

A: Given that  fx =a2-x2if  0 &lt; x &lt; a0if   x &gt; a The Fourier integral of f(x) is given by…

Q: Let f(x)=2 cos(5x)+3 sin(4x) and let q, be the Fourier polynomial of degree n for f. (a) Show that…

A: Given: fx=2cos5x+3sin4x The period is 2π as f2π+x=fx The fourier polynomial of degree n is:…

Q: State the definitions of direct and inverse Fourier transforms. Then, compute the Fourier transforms…

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Q: 3. a) Find the Fourier transform of g(x) given that g(x) = 3e¬4|x+2| b) Using the formulas for…

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Q: { x2, Ix1 a ||

A: Given function is f(x)=x2     x&lt;a0      x&gt;a let the Fourier transform of f(x) is F(s) So we…

Q: Suppose the function f: R→ R has Fourier transform 1 f(p) = e-p². 1+ 4π²p² i. What is the Fourier…

A: As per the question we are given the Fourier transform of a function f(x) as f̂(p) From that we have…

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

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Q: Q1) using Fourier transform find x(t) below x(t) = [e-3tu(t) * e-6*u(t)] dt

A: Solution is given below

Q: A function f(t) has Fourier transform, F(w) we. What are the Fourier transforms of: (a) f(t-3) (b)…

A: If F(ω) is the Fourier transform of f(t), then using the property of shifting, it can be written…

Q: Problem Find the Fourier coefficients of the function: (-5 0 ≤t ≤ 1/7 y(t) = 5 <t≤ and y(t +π) =…

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Q: the Inverse Fourier Transform x(t) of each signal X(w) given below. X(w) = -4 sinc² X(w) = πd(w − 1)…

A: "Since you have posted multiple questions, we will provide the solution only to the specified sub…

Q: find the derivatives complex funcation. {tanh¬'(iz +2)}-1,

A: fz=tanh-1iz+2-1=1tanh-1iz+2 It is known that tanh-1x=11-x2 so it follows:…

Q: Find the Fourier integral representation of the function f(x) = {1x1₁ |x T

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Q: 50, dex(+) = -25 (+ + 2) + 25 (1-0) + 15 (t-1) at 2 = -√(x + 2) + 251f) + 5lt-2) By using…

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Q: The non-periodic function f(x) is defined by f(x) = e-l=l. Obtain the Fourier transform of f(x).

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Q: ) If F(ƒ) = ƒ(§) is the Fourier transform of f(x), show that the Fourier transform of x f(x) is…

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Q: Find: x - 4x + 13x = 2 sint, x (0) = 1, x(0) = 0 (a) Obtain the solution to the ODE by solving for…

A: Solution of the differential equations using Lapalce transfermation and homogeneous method