Use the an appropriate Fourier transform to find the vertical vibrations u (x,t), of an infinite long string which initially has the shape of the function f (x) with initial velocity g (x) unit wave speed. Assume that f and g have Fourier transforms. (Explain all your steps).

Q: Find the finite cosine transform of 1 – where 0<x< T.

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Q: Use the Laplace transform table and the linearity of the Laplac- transform. t+sinv 7.2 2.2 7.2

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Q: Use the Fourier transform to solve the BVP Urr + Uyy = 0, -0 0 u (x, 0) = f (x) lim u (æ, y) = 0,…

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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: DEFINITION

A: We will find the Laplaces Transform.

Q: Find the third-order Fourier approximation of f (x) = x, 0 ≤ x ≤ 2π.

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Q: Find the Fourier transform of S (x) =!-\,| sin x dx Hence evaluate

A: Given,    f(x)= 1-x, x≤10        , x&gt;1

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: Apply the theorem of integration of transforms to find the Laplace transform of f(t)=2sin5t. Show…

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Q: Find the laplace transform of et

A: See the attachment

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: / find the fourier transform of the function eat tく。 SCt) = -at

A: The given problem is to find the Fourier transform of the given function S(t).

Q: Use Laplace transform technique to solve y +2y +2y= e-, y(0) = - 4, y'(0) = - 2

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Q: Obtain the laplace transform of

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Q: Find the Laplace transform of this function by expressing it as a combination of the functions you…

A: The Laplace transform of the function is represented as , it is defined as , since the dimension of…

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

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Q: Find the Fourier approximation with the specified order of the function on the interval [0, 2π].f…

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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: f(t) = [1– u2m(t)](2 sin t – sin 2t) U2n

A: Some of the properties of Laplace transformation Lsinat=as2+a2Luc(t)=e-cssLuc(t)g(t)=e-csL[g(t+c)]

Q: the Fourier transform of a continuous time signal x(t) is X(ja), then, the Fou ansform of the signal…

A: Given, Fourier transform of a continuous-time signal                                   x(t)  ↔…

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: f *g =g *f , where (*) is the convolution in Fourier transform. Select one: True False

A: Given: (*) is the convolution in fourier transform. To prove:  f*g=g*f. Proof: It is known that…

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: Find the fourier transform of: | coshw,t

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

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Q: Find the sine Fourier transform for f (x) = sin æ, x < 0,

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

A: Given function is,

Q: Show that the finite sine transform of , 0 < x < n is (- 1y*'- p

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Q: Determine the Laplace transform of the function tcost using the 2nd derivative theorem.

A: Laplace Transform: Given a function ft defined for all real t≥0, the Laplace transform of ft is a…

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

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Q: Find the Laplace transform of f (x) = 3 sin 3x – 2e-2x

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Q: Show how to do the Laplace transform of f(t) = t*cos(w*t) using the table of operational transforms.

A: Given  f(t) =t cos ω t

Q: i) Find the Fourier sine transform of (sinx, 0a %3D au Courier Transforms, Calculate

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Q: Find the Inverse Fourier transform of Te-lw||

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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: Find the finite cosine transform of f (x) if ƒ (x) = -x+ in (0, t).

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Q: Show that (a) L-1 = sin(at) - tcos(at) %3D (s²+a²)²) (where L indicates imverse Laplace transform)…

A: L-11s2+a22=12a2sin(at)-12a2tcos(at)

Q: Solve by using Fourier transform method. Ha.

A: Given: By using the Fourier transform method uxx+uyy=0, -a&lt;x&lt;a, 0&lt;y&lt;∞,   uy(x, 0) = γo,…

Q: nsform of f(t) = et-T sin 2rdr. %3D

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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: Find the Fourier-sine transform of ƒ(x) = |x − 3| − |x − 2| + 1. -

A: We will first compute the complete Fourier transform of f(x) then using Euler's formula and…

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

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Q: Solve for the Laplace transform of the function 8cos(at) and then solve for the value of a. Show…

A: Topic:- Laplace transform

Q: show that the Laplace transform of f(t)=te^(at)

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Q: Find the Fourier cosine transform of e-x.

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