Q1) Find Fourier transform for the following functions: a) x(t) = 3 + (sin2wt)² b) y(t) = 5. (e-6t). 8(t – 8) + 6u(t + 8) %3D

Q: 10. Solve the following IVP using Fourier Transform: -00 0, u(x,0) = e, -0 <r < oo.

A: Given ut=uxx, -∞&lt;x&lt;∞, t&gt;0u(x,0)=e-x2, -∞&lt;x&lt;∞

Q: 1 (b) Find Fourier cosine transform of f(x)=< -1 <x< 0<x</

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Q: Find Fourier transform of i 1x ka f(x) = 1₁ 0 Ixl ya Then find: 05- Sin Pa Cospx dp , P of M.H sin…

A: Fourier transform of the function and deduce the given definite Integral

Q: Find the Fourier Sine Transform of e-t and hence find the Fourier Cosine Transform of te-t.

A: Fourier sine transform of e-t is ∫0∞e-tsinωtdt. Calculate it:  ∫0∞e-tsinωtdt=∫0∞e-teiωt-e-iωt2idt…

Q: (11) The Fourier cosine transform of the function f(x) e; x>0, is

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Q: Find the Fourier transform off (x) defined by Example 6. 1, |x| a f(x) = sin s ds (ii) 00 sin sa.…

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Q: Find the sine transform of a function of x which is equal to sin x for 0 <x<a and 0 for x2a.

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Q: e> and deduce that Find Fourier sine transform of- ar e bx e | sin px dx = Tan2 - Tan a

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Q: 8 The inverse Laplace transform of the function is sin(3t) (A) t – 3 sinh(3t) (B) t- 3 sin(3t) (C)…

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Q: Suppose an undamped forced spring mass system is driven by the equation + 9x = f(t), dt where the…

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Q: Find the Fourier sine expansion of f(x)=x² (3L– 2x) on [0, L].

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: What are the coordinales of T for the transformmation (T-3, 1) D.XATUV) of T(-7,-6), U(-8, 3), and…

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Q: The best approximation of f(x) = cos(8 + x) by a Fourier polynomial of degree 1 is

A: The Fourier Polynomial of degree n is Fn(x)=a0 + ∑k=1nakcos(kx) +∑k=1nbksin(kx). Then, the Fourier…

Q: IS kept contact with ice at 0°C' and if initially the rod is submerged in hot water at 100°C. Use…

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Q: 8.(a) Find the Fourier transform for the function cos x, -n/2 7/2 f(x) = 0, (b) Use the result in…

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Q: { 1,-< |x| < = (0, anywhere else 2. Find the Fourier transform of the function f (x) =

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Q: 1. Use the differentiation and integration properties of Fourier Transform to find a closed form for…

A: We have, xt=0             t&lt;-12t+12     -12≤t≤121                t&gt;12      Apply Fourier…

Q: (k) f(x) =X[a.b](x) eiaz,

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Q: 27. Explain why this function does or does not have a Fourier transform. If it does, compute its…

A: Consider the given function. fx=0,        x&gt;1excosx,x&lt;1 Fourier transformation is defined as.…

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: Q4/ Use odd and even function properties to find Fourier Transform for the following function as in…

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Q: (1-1z1, 1리1

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Q: b) Find the Fourier sine transform of f(x) = 12π, 0 < x < 6π

A: Fourier coefficients represent the amplitude of each harmonically-related sinusoid present in the…

Q: Solve for the Laplace transform of et sint cost cos 2t cos 4t 7+4s+20 82-4+20 -4+68 4s+8

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Q: Find the Fourier transform for S(2)%3D sin a, 2 0.

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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: f(x)= == ¹xcl! Obtain the Fourier transform of

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Q: y' = 8x x(0) = 1 %3D x' = 2y y(0) = 0 %3D

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Q: Find the Laplace transform of the f(t) = 8t° e2t – 3t cos(t) + 10. Explain the solution steps in…

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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: Solve the IVP x”+9x = U(t-2)sin[3(t-2)], x(0)=2, x’(0)=0 using Laplace Transforms. Identify xc , xp…

A: The solution is given as

Q: a) Find Fourier Transform f (x) = |x| > B and Evaluate Sin[2B]Cos[2x] da -8-

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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: 8. Find the 6th order Fourier approximation of the function that is periodic and f(x) = x, -2<x <2

A: Given function is fx=x ,   -2≤x≤2 Compare the interval  -2≤x≤2 with -L≤x≤L, we get L=2…

Q: 2T (-1Y- Find f(x) if its finite sine transform is given by f, (p) = where 0<x < T. -, p = 1, 2, 3,…

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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: find 2d Fourier transform of e^(-4pi*(x^2+y^2)) the answer is e^(-pi(x^2+y^2)/2) why?

A: Find the 2d Fourier transform of the given function and the 2D transform of f is defined by the…

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

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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: [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: a)find fourier transformation f(x)=x in range (0,10L) b) find fourier transformaion Slx) in range_3…

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Q: Find z-transform for the functions (using properties) 1) x(t) = eat cos (w t)

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: 5 The inverse Laplace transform of the function sin(2t) (A) 1 – 2 sinh(2t) (B) t- 2 sin(2t) (C) t- 2…

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Q: (7) Find the Fourier transform of the following functions: { {: cos x, if 0 1 (ii) f(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 f(t)=6t6e2t-3t cos(t)+10 Explain the solution steps in your own…

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Q: 27. Explain why this function does or does not have a Fourier transform. If it does, compute its…

A: The given function: f(x)=0,             |x|&gt;1excosx,   |x|&lt;1 This function have a Fourier…

Q: 3. Find the Fourier transform of f(x) = {1, |x| 1 Also evaluate .00 Sinx dx

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