Solve the following initial value problem using Laplace transform: d²y dt² 18 dy where +45y = g(t), y (0) = -1/3, t-o=9, 3 0 < t < 6 6 6 ≤t g (t) Let Y (s) be the Laplace transform of the solution y (t). Then evaluate Y(-1/3) y (-1/3). Y(−1/3) · y (−1/3) =( )

Q: Find inverse Fourier transform of F(W) %3D W2-2W+3

A: A complex domain function can be transformed into a real-time function through the inverse Fourier…

Q: Find the inverse Laplace transform of the function as + b H(s) = (s – a)2 + 32 °

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

A: Given,    f(x)= 1-x, x≤10        , x&gt;1

Q: Q3: Find the following Fourier Transform using properties only: F{e=2t+6+j2(t=3)u(t – 3)}

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Q: 3 Find the inverse Laplace transform for (s-2)2+9 (a) e-2t sin3t (b) e2t sin3t (c) 3e-3t sin2t (d)…

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Q: f(t)=u(t-3)(t-3)e-4t Obtain the Fourier transform of the function

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Q: e^3(t+2)/2. Find laplace transform of the function

A: Let's find Laplace transform of given function.

Q: 6. a) Find the Fouriér Transform of f(x) = 1-x² (x) 1), b) Evaluate, - I Cosx-sinx cosdx

A: We have to solve the given problem using Fourier transform.

Q: The Fourier transform of the function f(t) = 2e-2t cosh 2t u(t)is: 2 4 A- πδ (ω) B- πδ(ω )+ j2w+w?’…

A: We have to use formula for Fourier Transform.

Q: • Let: X₁ (jw) = 2nd(w) + nd(w − 4ñ) + ñ8(w + 4π) • Use the inverse Fourier Transform to find x₁(t)…

A: Introduction: Like other integral transformation, Fourier transformation has also its inverse. In…

Q: Find Fourier transform for the following functions:x(t)=3+(sin2wt)2

A: Given function is, xt=3+sin2wt2.      ........1 Fourier transformation: Fourier transformation of…

Q: -Obtain the Fourier transform of f(t): = sin (30) -t²+7it+12

A:

Q: Determine the Fourier transform and plot the magnitude S1, It| < T/2 l0, otherwise (ii) x(t) = f(x)…

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Q: If F(w) is the Fourier transform of f(t), then the Fourier transform of g(t) = -e3it f(t) may be…

A: Here, gt=-e3jtft

Q: Use Laplace transform technique to solve y+2y+2y=e, y(0) = 3, y (0)=-3

A: We need to use Laplace transform to solve this differential equation.

Q: Find the convolution of f(t) = 3t and g(t) = sin (21). You can either calculate f * g directly, or…

A: In the given problem we have to find the convolution of two function f(t) and g(t) using the…

Q: Find the fourier transform of f(t) = e-2(t+4)ʻ sin (nt).

A:

Q: 3. (a) Calculate the Laplace transform of each function. Explain your reasoning (i) cos(2t) sin(4t).

A: according to bartleby guide line we do only first part of multiple questions please re post other…

Q: Find the fourier trans y (t) = x (+). Cos wot

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Q: The first: find using transform i x =rcos(0), y=rsin(0) 00 00 e-(7x²+3y) dxdy

A: We have to use the given substitution.

Q: Find the Fourier transform of f(t) = 5e-3|t|_ %3D

A: To determine the Fourier transform of the below function. ft=5e−3t

Q: Find the Inverse Laplace transform of F(s) = 8Bs 7C (s + 3) (s - 4) (As − 1)

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