Calculate the Fourier transforms of the following functions (you do not need to use any complex contour integration ): i) e-alæl, a > 0. (Hint: Use direct integration.) ii) e-ax? , a > 0. iii) cos(x)e-. (Hint: cos(x) = Re ei" .)

Q: What is the Fourier transform of the function 4 cos(5t) on the interval [-x, a]| Select one: O a. 4…

A: Here we have to find the Fourier transformation of the function x(t) = 4 cos (5t) Using the formula:…

Q: 5. Determine the Laplace transform of tet sin? t using any methods introduced in the module.

A: Given ft=te4tsin2t

Q: To find the Laplace transform of eª sinh(at) you would substitute into which gives

A: Calculate the Laplace transform of e9tsinh(at). Le9tsinhat=Lsinhats→s−9

Q: (a) Compute the integral 7² ſ tri(t)e¬j¤tdt [Hint: Fourier Transform.] use Fourier transform tables…

A: Since you have asked multiple question.As per Bartleby's rules I will answer only first question.If…

Q: Find the Laplace transform of: 1. f(t) = e(-3t) sin(2t) cos(3t) cosh(t)

A: Given that 1) f(t) = e-3tsin (2t) cos (3t) cosh (t) 2) f(t) = 1+sin t + (8t)15 + t2cos 3t We have to…

Q: Use the tabulated integral J eax cos bx dx: (a cos bx + b sin bx) + C to obtain L{coskt} directly…

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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: Find the solution of the differentical equation using Laplace transform +64 dt given that %3D 남 (o)-…

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Q: Find the Laplace Transform of: e-2 -2t sin2t + e3tt2

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Q: Derive the general formula for the Laplace transform of sin bt.

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Q: 1. Find the Fourier transform of this rectangular pulse X (w) and show that sin πωτ X(w) = A² 2.…

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Q: 7. Given that the Laplace transform of te is F(s) =- (s + k) Laplace transform of te" without using…

A: The solution is given as

Q: WHAT IS THE FOURIER EXPANSION OF THE PERIODIC FUNCTION WHOSE DEFINITION IN ONE PERIOD IS: F(t) = for…

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Q: 3ヒ Sinh-

A:

Q: FIND THE FOURSER . COSINE FRANSFORC? OF tix) = 11 2. 1+x² Hence DERS VE FOURLER IRAS SINE transForm…

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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: Find the laplace transform of 1. f(t)= cos(5t)cos(2t) - sin(5t)sin(2t) 2. f(t)=…

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Q: Use the Laplace transform to solve the given initial-value problem. Use the table of Laplace…

A: Given differential equation is  y''+25=cos(5t) with initial conditions y(0)=3 , y'(0)=2 we have to…

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

A: By Bartleby policy I have to solve only first one as these are unrelated problems.These are…

Q: Use Laplace transform to solve the given IVP. 3. у" — у' %—D еХ cos x, у(0) %3D 0, у'(0) — 0

A: We have y''-y'=excosx  , y0=0 , y'0=0 Now,  Ly'=sYs-y0Ly''=s2Ys-sy0-y'0 Take Laplace transform on…

Q: Use the Fourier sine transform to solve the following BVP with 0 0 10₂4+02=0, მყ2 u(0, y) = 0, u(π,…

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

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Q: Use Theorem 7.4.2 to evaluate the given Laplace transform. Do not evaluate the convolution integral…

A: Let's find.

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

A: Explanation of the answer is as follows

Q: solve the following equation using laplace transforms: note:= 1 not 11 dx - 3 dx + 2x = 0, x(0) = 0,…

A: Given d2xdt2 -3dxdt + 2x = 0                                    (1)x(0) = 0…

Q: (3) A signal has Fourier transform as, 1 sinc (2w X(w) sinc + 2. Compute x(t)

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Q: Solve for the laplace transform of e^(at) cos bt using using the integral formula for laplace…

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

A:

Q: 5 sinh 3t + 4cosh 3t

A: Suppose ft=5sinh 3t+4cosh 3t Definition: The Laplace transformation of ft is a function of a new…

Q: A truncated cosine wave { cos3r, y = f(x) 0, otherwise. Find the Fouri er transform.

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Q: Determine the Fourier expansions of the periodic functions whose definitions in one period are: 0.…

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Q: 2.) cos (10t+1)

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Q: FInd the Laplace transform of cos t cos 2t cos 3t

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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: Use the Laplace transform to solve the following IVP y - y = 2 cos 5t, y(0) = 0 %3D

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Q: Find the Laplace transform of sin 21, 0<t < 2n S(): 0, 12 2n

A: we have given the function f(t) = sin2t,  0≤t≤2π   0,          t≥2π we have to find the Laplace…

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: a Find the Fourier transform of the signal x(7) = 2 cos(m)[(1+3)-(1-3)], using the Fourier integral.

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Q: What is the Laplace transform of 7sin (6 t) sinh(6 t)

A: What is the Laplace transform of 7sin (6 t) sinh(6 t)

Q: 4. Use the dilation principle to find the Laplace transform of 1- cos 5t cos t given L{- In g² +1 t

A: We want to find Laplace transform of 1 - cos5tt Given L1 - costt = 12lns2s2+1

Q: Prove that the Laplace Transform of ´cos(bt) is S-a (s-a)° +b² Please show your solution clearly.

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Q: The Fourier Coefficient bn is given by.... bn 1/m fx) cos nx dx bn f(x) cos nx dx bn= f(x) sin nx dx

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Q: Solve for the laplace transform of e^(at) cos bt using using the integral formula for laplace…

A: The solution is given as

Q: (b) Using Laplace transform, evaluate te -2t Cos 2t dt 0.

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Q: 5. * + 9x = cos 2t

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Q: The Laplace transform of L[2 sin 5t sin 4t] is

A: Laplace transform can be solved by using trigonometric identities and Laplace transform of…