f(t)=(e^−4t−e^−t)^2

Q: Find the linear transform which converts inside the circle has a radius 2 and center is (0,-2) to…

A:

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: The Laplace transform of L(sin5t) is

A: We will use the definition of laplace transform to find the laplace transform of L(sin5t). Laplace…

Q: What is the Laplace transform of 2?

A:

Q: メ - Hx = 8 ; t-0,メ=? %3D

A: Given x.-4x=8  at t = 0 , x = 2

Q: Determine the Laplace Transform of sin³3t

A:

Q: ut

A:

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

A: Given,    f(x)= 1-x, x≤10        , x>1

Q: The general solution of the initial value problem given below is the "Laplace Transform". find using

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 of x3

A: Given : To find the Laplace transform of x3

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

A:

Q: Find the Fourier transform of -at TE|< 1 fCE) = otherwise

A: We have to solve the given problem.

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

A:

Q: find the fourier transform of logx u(t)

A: Unit step function: u(t)=1t≥00t&lt;0 Fourier transform of a function fx is  Fp=∫-∞∞fteiptdt…

Q: Use differentiation in time domain to solve the the Laplace transform: y"-y'-6y=0; y(0)=6, y'(0)=13

A:

Q: Find the Laplace transform of (te-2cost)

A: Use property of Laplace transform

Q: fCt = [ Htu (t-π) Jun (37)

A: As per the question we are given the following function : f(t) = [1+u(t-π)]sin(3t) And we have to…

Q: By using convolution theorem for Laplace transform, prove that 1 L-1 + x}={erf (2√x) PVp +4

A:

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: What

A:

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: Find the Laplace transform of equation.

A:

Q: 5 sinh (3t) +4 cosh (3t)

A:

Q: Solve for the laplace transformarion of the given function

A: the Laplace transform, named after its inventor Pierre-Simon Laplace, is an integral transform that…

Q: In general, if two functions have the same Laplace transform, these functions cannot differ over an…

A: Solution

Q: Laplace transform of the convolution integral of

A: Note:- Convolution Integral Theorem:- If function ft  and  gt are the piece-wise continuous function…

Q: 2. Determine the Laplace transform of the given function using the Table coshbt te3t sin2 t

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

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Q: The Laplace transform for ramp function with a time delay can be expressed as follows: *

A: Let the time delay is T, So the ramp function will be f(t)=(t-T)u(t-T) Where u(t-T)=1, t&gt;T0,…

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

A:

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 the Laplace transform by the method of definition.

A:

Q: Solve the initial value problem using the Laplace transform.

A: Given initial value problem is y'''(t)+5y''(t)+9y'(t)+5y(t)=t2ety(0)=0, y'(0)=0, y''(0)=-2…

Q: sin(2t) cos(2t)

A:

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: If a function "f" is not piecewise continuous on [0, infinity), then its Laplace transform will not…

A: True

Q: sinh³ 4t

A:

Q: Using Laplace Transform, solve the following initial value problem Зу' - 4y — sin 2t У) --

A:

Q: times the Fourier transform of f(x) provided that the first (n – 1) derivatives of f(x) vanish as…

A:

Q: Determine the Fourier transform of f if f(x)=e* for x> 0 and f(x)=sinh2x when x< 0.

A:

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: 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: Laplace solves the Initial Value Problem Find by transform.

A:

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

A:

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: 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)