Find the cosine transform of a function of x which is unity for 0 < x < a and zero sin ap , for x2 a. What is the function whose cosine transform is

Q: Use the definition of Laplace transform and Euler's formula to find the Laplace transform of cos t…

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Q: Determine the transform of the following functions using any methods . 2a sin 4t + 4b cos 3t

A: Some Laplace transform formulas: L{sinat}=aa2+s2L{cosat}=sa2+s2 Some properties of Laplace…

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: Find the Laplace transform of: (a) cosh at (b) sinh at

A: Given (a)cosh at  and (b)sinh at We have to find the Laplace transform of them…

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

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

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

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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: 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: Determine the transform of the following functions using any methods. 2a sin 4t + 4b cos 3t

A: See the attachment

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

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Q: Find the cosine transform fe(w) of f(x) for f (x) = -6 if 0 2. f.(w) %3D

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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: 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: Find the Laplace Transform for the function e-Nt sin² (Nt)

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Q: Determine the Laplace Transform of cos*t

A: cos3t≡(cost)(cos2 t) cos3t=cos(1−sin2 t) cos3t=cost⋅1/2(1+cos2t)…

Q: ii) using the Fourier Transforms, Calculate dx. Jo (4x*)(9+x*)'

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Q: -t cos(3t

A: To solve this problem, we  use the  result of laplace transformation.

Q: Find the transform, indicating the method used and showing the details (sin wt) (cos wt)

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Q: x(t)=sin(t-3T)

A: Z transform

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

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Q: Find the Laplace Transform of the following function. 10e-5t sin 2.

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Q: e2t+a (2 cos at – 3 cosh 2at) -

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Q: 4. e2t+a(2 cos at – 3 cosh 2at) -

A: It is given that the function ft=e2t+a2cosat-3cosh2at. We have to find the Laplace transform of ft…

Q: Solve for the Laplace transform of sint sin 2t cos t

A: The given function is f(t)=sin t sin2t cost  rewrite the function as  f(t)=122sin t cost sin2t…

Q: Determine the Laplace transform of L(sinh 5t * cos t)

A: Explanation of the answer is as follows

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

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Q: Find the cosine transform of a function of x which is unity for 0 <x < a and zero sin ap, for x 2 a.…

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Q: Find the fourier transform of following signals a. x() = cos (2xf.1) b. x(1) = sin (27f 1) c. For…

A: Calculate Fourier transform of cos22πfct: Fcos22πfct=F122cos22πfct-1+1…

Q: Solve the laplace transform of f(t) = sin (10t). Hint: You may convert the given to whichever form…

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Q: Determine the transform of the following functions using any methods. e3t sinh 3t

A: We will calculate the Laplace transform of the given function . We have the following definition of…

Q: Find the transform of the given function by use of a table. f () = | = cos -4t - sin -4t

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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: The German mathematician Karl Weierstrass (1815-1897) noticed that the substitution t = tan(x/2)…

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Q: Find f(x) if its Sine Transform is Hence find F, ().

A: Given that f(x)=e-axx The fourier sine transform is  Fs=∫0∞f(x)sinsxdx=∫0∞e-axxsinsxdx…

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: Solve the Laplace transform of: 3 cos 8t + 2 sin 8t

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

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Q: Find ℒ{sin(at)}. For what values of s is this transform defined?

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Q: Find the exponential transform of the function {1, Pi/2<x<pi. and 0, otherwise} and write f(x) as a…

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Q: Q1: Find the fourier expension of the periodic function whose defination in one period is: 0<x<3 3…

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Q: · findd the fourier sine transform of f(x) = 7 A 9x 0<X<9 otherwise

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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: Find the Fourier transform of the following function: 7 sin(3r – 2) r2 + 25 - 2 exp (4 - 5|r-3|).

A: We are given a function in variable x and we have to find its Fourier transform. For that we will…

Q: f (x) =| , where 0<x<T

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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 transform of the given functions by use of the table. f(t)= cos 3t-sin 3t

A: Lcos3t-sin3t=Lcos3t-Lsin3tUse Laplace Transform table:          Lcosat=ss2+a2,…

Q: Solve for the inverse Laplace transform of O 4cos at - 3 sin at 4 sin at – 3 cos at 3cos at - 4 sin…

A: It is known that: L-1a·fs+b·gs=a·L-1fs+b·L-1gsL-1ss2+a2=cosatL-1as2+a2=sin(at)