4. Solve the following equation by transforming the Method Laplace (Transform) transform. u(x)= x - f (x −1 )u (1)dt

Q: A function f (t) = e-at is defined for a > 0 andt > 0. By finding the Fourier transform show that…

A:

Q: Find Laplace transform of x(t)=t (cos)^2 (wt)u(-2t). *

A:

Q: Q2. Find the Fourier transform of the function S2x e- 0<x <1 otherwise f(x) = %3D

A: The given problem is to find the Fourier transform of given function, we have to use Fourier…

Q: Consider the following ODE: 7* + 5x = 39(t) a. Solve for x(t) using the Laplace transform method.…

A:

Q: (2) Find and draw the Fourier transform of f (t) = %3D 9+t2

A:

Q: Q1/ Solve the following equation using Laplace Transform, when y(0) =0, and y =2 y-3y+2y3D2t

A:

Q: 2. F(s): = 3s² +5s-4 S4

A:

Q: Determine the Fourier transform of the given function: t, 0 < t < 1 0<t<2 f(t) = 2t - 1, 0,…

A:

Q: Find the inverse Laplace transform of 1 G(s) = s2 – 4s + 5

A: Given,

Q: Given y(t)=t²e+t. The above equation can be transform by using 1. First shift theorem 2. Second…

A: Given  y(t)= t2e4t

Q: Solve the fourier transform of the following functions: 2ix if-1 < x < 1 otherwise 1. f(x)= = {e²

A:

Q: 3y +y = 3y2 Inx

A: ANSWER :

Q: e inverse Fourier tra |w| e 2 3 N

A:

Q: 8. Find the function whose Fourier sine transform is the following function. S[u] - 2 0 x = [1, 2],…

A: Given: Fourier sine transform is given as Su=2x∈1,21x∈(2,3]0otherwise. To find: The function which…

Q: 5. The fourier transform of the function f(x)=eI, is 2 4- w? O b. 2 w? -4 4 С. w? - 4 Od. 4+w? 4.

A:

Q: If the Fourier transform of f(t) = is F(w), express the Fourier transform of g(t) = 2 0<t<1 0…

A:

Q: Suppose solving an equation by Laplace transform results in 6 s Y(s) = s² + 64° Evaluate y(").

A: y(s)=ℒ(6ss2+64) =-3(2si(8s)-π)sin(8s)-6cos(8s)ci(8s) y(π)=-3(2si(8π)-π)-6cos(8π)si(8π)

Q: 5. Determine the following transforms. b. L{cost 8(t – 37)}.

A:

Q: I have not yet been taught Laplace Transform by my lecturer, I believe. Isn't there another way…

A:

Q: If f(t) = 1; Itsa 0; |t| 2 a ; then find the Fourier Transform of f(t).

A: Given f(t)=1, t≤a i.e., -a≤t≤a0,t≥a i.e., t≥a &amp; t≤-aFourier Trasnform of f(t) is:…

Q: Find the inverse Laplace transform of (s+7)/(s²+4s+13)

A:

Q: If F(w) is the Fourier transform of f(t), then the Fourier transform of g(t)=4e³jt f(t) may be…

A:

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

A:

Q: Compute for the inverse Laplace transform of Y (s) = (s+2)³ * 3 e-2t+2 e-2tt e-2442

A:

Q: If F(w) is the Fourier transform of f(t), then the Fourier transform of g(t)=3e²jt f(t) may be…

A: If Fω is the Fourier transform of f(t), then using the linearity property, it can be written that…

Q: 3. Determine the Laplace transform of f(t) = uz(t)(t − 3)³e²−3.

A:

Q: 1. v₁ = (4, −2, 6, −4), V₂ = (6, −3, 9, −6)

A:

Q: Use the definition of Fourier Transform, i.e. the equation f(t) = LF(@) elatdw to find the Fourier…

A: Using the given definition f(t) =12π∫-∞∞F(ω) e j ω tdω we have , F(ω) =12π∫-∞∞ f(t) e -j ω tdt…

Q: 2. Obtain the Inverse Laplace transform of the function: S³ + 3s² + 2s + 1 (s + 2)(s + 1)² F(s)= =

A:

Q: Find Z transform for 3 F(t) = t * * F(t) = u(t-2)

A: Given that F(t)=t3 F(t)=u(t-2) We have to find the Z transformation of f(t).