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.

Q: 4. Solve the following equation by transforming the Method Laplace (Transform) transform. u(x)= x -…

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Q: e-2t cos 3t cOS

A: The given question is related to Laplace Transform. The solution is explained below.

Q: 40. Find the inverse Fourier transform off (p) = e¯ ™ Y.

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Q: 5- Which of the following is the inverse Laplace transform of the function X (s) = s+ 4s +8 -2t cost…

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Q: 8 The inverse Laplace transform of the function is sin(3t) (A) t – 3 sinh(3t) (B) t- 3 sin(3t) (C)…

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Q: Find the inverse Laplace transform of (s – 2)e-s s2 – 4s +3 | F(s) =

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Q: (b) Find the Fourier transform of the function given below 1– x? if |x|1 and hence find the value of…

A: Calculate Fourier transform: Fω=∫-∞∞fxe-iωxdx         =∫-111-x2cosωx-isinωxdx…

Q: Find the Fourier transform of ƒ (t) = 2 for -T≤t≤0 2 for 0 ≤ t ≤T

A: We have to solve given problems:

Q: By using the Fourier transform, find a solution for the following problem (PJu,(1, x) = ux(!, x) +…

A: The partial differential equation given is as follows: utt, x=uxxt, x+3t2 Apply the Fourier…

Q: 7. Obtain the Fourier sine transform of the following functions: sin wx (c) x² +1' w > 0

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

Q: Determine the Laplace transform of e-5t sinh(6t) · е s+5 s2 – 10s–11 6. s2 – 10s-11 s+5 10

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Q: 3) Find the Fourier transform of the following signals L. x(t) x(t) + 3 + 2 -2 2 -1 -1 1 -2 using…

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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: 3s+2 4. s² – 8s +25 5s2 +8s – 1 5. (s+3)(s²+1) |

A: Given Laplace Equation 4.) 3s+2(s2-8s+25) 5.) 5s2+8s-1(s+3)(s2+1) linearity property of inverse…

Q: Find the Laplace transform for -4 f(t) = e'sin2t + e¯'cost 2 s + 1 2 s + 1 + s + 2s + 5 s - 2s + 2 2…

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Q: What is the inverse Laplace Transform of a function y(t) if after solving 32-s+3 Differential…

A: Given To determine inverse Laplace transform of a function y(t) Using inverse Laplace transform…

Q: 10. Solve the following IVP using Fourier Transform: -00 0, u(x, 0) = e¯**, -00 <x < o0. %3D

A: Given: Let us consider the given, ut=uxx,              -∞&lt;x&lt;∞,   t&gt;0ux,0=e-x2,…

Q: find the inverse Laplace transform of the given function. 3.F(s)=2s2+3s−4F(s)=2s2+3s−4

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Q: 7s2 – 3s + 26 F(s) (8 – 1)(s² + 9)

A: Explanation of the solution is given below...

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: (1, |x| 15 Q.1 Find the Fourier transform of f (x) defined by f (x) = %3D Hence evaluate S: sins…

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Q: S1 -x, xl 1 Find the Fourier transform off(x) = and hence evaluate sin x) Cos 2 X COS X – dx.

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Q: Find the inverse laplace transform of : -S -2s 1– 2e + e F(S) = (6? + 4) (s)

A: To Find the inverse Laplace Transform of given Problem first we will use the linearity property then…

Q: What will be the numerical coefficient of cos(V3t)etin the Inverse Laplace Transform of 3 s(s3-8) O…

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

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Q: The inverse laplace transform of 3s2+4/s(s2+4) is A. 1+cos 2t B. 1+3cos 2t C. 1+2cos 2t D.1+3cos t

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Q: 2) Find the (complex) Fourier transform of 1-2, if r| S1, F(z) 0. if |피> 1, I COS I- Sin z and hence…

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Q: (c) Compute the inverse Fourier transform for the function ={ Is| 4 -s, F(s) 0,

A: The given function is  F(s) =        - s             |s|&lt;= 4         =           0.…

Q: 2)Find the fourier transform for the function 0 <t < 2 1 f (t) = {0 %3D otherwise

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Q: (7) Solve the PDE by Laplace Transform a²w aw <=100 +100 + 25w, ar² at w(x, 0) = 0 if x ≥ 0, we(x,…

A: The given P.D.E is                       ∂2w∂x2=100∂2w∂t2+100∂w∂t+25w,wx, 0=0 if x≥0, wtx, 0=0 if…

Q: 7. Find the Fourier sine and cosine transforms of the following functions defined on [0, ∞). x =…

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Q: Find the Fourier Transform of Sa? – x², for |æ| a f(x) = and hence deduce that (sin s- s coss -) ds…

A: Fourier transform of gx=1 for x&lt;a0 for x&gt;a is ∫-aa1.e-isxdx. Calculate it:…

Q: Find the Laplace Transform of e-t sin2t 2 2s 2 A. ²/+ B. S (s+1)²+4 (S-1)²+4 C. S+1 s(S²+4) D. None…

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Q: 3.48. Find the Laplace transform of x(1)=(e" cos 2r – Se *ju(1) +*u(-1)

A: The given problem is to find the Laplace transform of the given time function. Given…

Q: 7. In the process of computing the inverse Laplace transform of the function F(s) = -23 - arctan ¹…

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Q: Q6) A-Show that: a) X(f)=X*(-f) 4 To/2 b) if x(t) is even, then b=0, ano/²x(t) cos(2πnfot) dt…

A: Solution : A) a) X(f)=∫-∞∞x(t)e-jftdt X*(f)=∫-∞∞x(t)e-jftdt* X*(f)=∫-∞∞x*(t)ejftdt…

Q: 1. Compute the Fourier transform of the following signal: x(t) = e-3|t| sin(2t)u(t)

A: Hint: The convolution theorem of Fourier transform states that, the Fourier transform of the…

Q: Q.2) Find the inverse Laplace transform of 26 – s2 - а) s(s² + 4s + 13)

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Q: Find the inverse Laplace transform of 5s + 1 F(s) = s2 – 7s + 12

A: F(s)=5s+1s2-7s+12       =5s+1s2-3s-4s+12       =5s+1s(s-3)-4(s-3)       =21(s-3)-16(s-4)(s-3)(s-4)…

Q: Determine the Inverse Laplace Transform of the functions using the Laplace of Integrals and…

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Q: I find the Laplaa Transform ) f4): e" (3t*+ 1) - 5 sin at 5 sin 3t

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Q: What is the inverse Laplace transform of Y (s) = (4s + 4)/ (s2 + 4s + 13)

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Q: 1 5. For a certain periodic function f(t) the Fourier coefficient b, kcosnt -k cosnt + n Jo b, when…

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Q: 12. Find the Laplace transform of the period function to f(1) = 2n-t <tS2n

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Q: Show that d() = ñ[6(w − K) + 6(w + K)] is the Fourier transform of cos (Kt).

A: To prove dw=πδw-k+δw+k is the fourier series of cos(kt)

Q: * Find the Laplace transform for -4 f(t) = e'sin2t + e'cost S s + 1 + 2 s¯ + 1 s* + 2s + 5 s - 2s +…

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Q: 5(a) Find the Fourier transform for the following function: f(t) = {e-31 0 . t> 0 ,elsewhere

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Q: If the exponential Fourier transform of f (x) = e-alxl 2a %3D a2 +b2 What is the Fourier transform…

A: considering the function fx=e-ax=2aa2+p2   fx=e-ax=2aa2+p2 and fx=e-bx=2ba2+p2

Q: (2) Find Inverse Laplace transform for; 3 1 (1)F(s)=- 3 (2)F(s)= s? +4 (3)F(s)= s (s +1) s (s² +16)

A: Find the inverse Laplace  as per our company guidelines we are supposed to answer ?️only first 3️⃣…

Q: Take the Laplace Transform of both sides of the IVP y'' + y = 2δ(t-1) w/ y(0) = 1, y'(0) = 1 and…

A: Step:-1 Note:- Some Laplace Transform 1. Lδt-a = e-as   for a&gt;0 2. Lyt=ys  and  L-1ys=yt 3.…