f) = (ae aet t<0 3) Find Fourier Transform for the following function as in figure:

Q: Find the Laplace Transform of f () =2 sin a +3 cos 2z.

A: This is question of laplace transform . Solution is given below

Q: Determine the Laplace transform of f(t) = 5sin 2t - 6t * cos 2t

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Q: (a) Find the Fourier transform of the function g: RR defined by Ste-kt, for t > 0, g(t) = otherwise.…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the Laplace transform of tan(t). Show your full steps Solution.

A: Laplace transform

Q: determine the laplace transform of t^2 sin 4t

A: We know that Lsin(at) = as2+a2 then Lsin(4t) = 4s2+42= 4s2+16 Also  Ltnf(t) = (-1)ndndsnLf(t)

Q: Find the Fourier transform of f if (e* jkax > 0 * ikax<0 Note : jika = if

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Q: Find the inverse Laplace transform of the following function by using convolution theorem. :(&+2)*…

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Q: t sinh 4t

A: We are given : t sinh 4t Now, L{sinh at}=as2-a2⇒L{sinh 4t}=4s2-(4)2=4s2-16 Now,   Lt sinh…

Q: find the Laplace transform of {t^2cost}

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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: Find the Laplace transform of 1. f(t) = [1 − u₂n(t)](2 sin t - sin 2t) - 2

A: Properties of the Laplace transform Laf(t)+bg(t)=aF(s)+bG(s)Lsinat=as2+a2Luc(t)sinat=e-css2+a2

Q: Solve for the Laplace transform of f(t) = 5 using long method. %3D

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Q: Find the Laplace transform of: 1. f(t) = e(-4t)[sin(2t) – cos(2t)]?

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Q: 3) x(t) te-at 1 4) x(s) = (Sta)2

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Q: Find the Laplace transform of: 1. f(t) = e(-30) sin(2t) cos(3t) cosh(t)

A: Given function can be written as ft=e-3tsin2tcos3tet+e-t2=e-3tet+e-t2sin2tcos3t

Q: Find the inverse Laplace transform of -6s e F(s) = s2 + 2s – 3 - - (Use for u.(t) .)

A: The given expression is Fs=e-6ss2+2s-3. We have to find the inverse Laplace transform of function…

Q: Find the Laplace transform of t cosh 2t

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Q: f(t) = 2t + 5et – sin 5t -

A: Given:  ft=2t3+5e4t-sin 5t To Find: The Laplace transform

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

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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: Find the Laplace Transform of (Non-anonymous questionO) f(t) = 2e3t sin 2t – 3e3t cos 2t -

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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: 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: d.-tte-6c 3

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Q: )Find the fourier transform for the function: - 1<t <1 otherwise 1 f(t) = {, | %3D

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Q: Give the Fourier transform of the function f. f(x) ha x € [0,₁] {* otherwise. =

A: Above question is solved.

Q: Solve X'= %3D 1 2. 人 2. Given use %3D -2-2 Laplace TransForm OF A to Compute At.

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Q: Laplace transform of sin(5t)u(t) is

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Q: Determine the Laplace Transform of e 12 cos v 7t + sinV5 - 3

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Q: Find the Laplace transform of 1. _ƒ(t) = ½ [1 − U2„(t)](2 sin t – sin 2t) - - 2

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: Find the Laplace transform using convolution theorem: Te2" sin(2(t - T))dr.

A: So, here f(t) = sin(2t) and g(t) = t e2t.

Q: Find Laplace Transform of f(t) = cos3t By DEF.

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Q: (c) Skctch x(t) = rect(2t)and solve for X(W). (d) Determine the Fourier Transform for x(t) in Figure…

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Q: Find the Laplace Transform of (t2 +4t + 2)et

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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: Determine the laplace transform of f(t) = sin8t sin 6t

A: We find the Laplace transform of  f(t)=sin(8t)sin(6t)

Q: f(t) = cos² 2t

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Q: (a) Find the Laplace transform of f(t) = te2" sin(2t). %3D

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

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Q: Find the Fourier scries of the function f(x) = |x| for -1 sx< 1. %3D

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

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

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Q: f(t) = 0, -1 <t<1 elsewhere

A: Given,         f(t)=ej2t, -1&lt;t&lt;1   0,  elsewhere

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

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Q: Find the Laplace transform of f(t) = te-t from the definition.

A: Here we use the definition of lapses transformation.

Q: transform

A: