Find the Laplace transform F(s) = L{f(t)} of each of the following functions. (i) f(t) = t^2 / 3 ( e^4t + e^−4t ) Hint – Use the Linearity Property and the Table of Laplace Transforms. (ii) f(t) = e^3t ( sin(t) + cos(t)) Hint – Use the Linearity Property and the Table of Laplace Transforms. (iii) f(t) = t( sin (2t) + cos (2t)) Hint – Use the Transform Derivative Principle and the Table of Laplace Transforms.

Q: Find the Laplace Transform F(t)=t^2e^(10t)

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Q: Find the Laplace transforms of the functions. f(t) = 3t^5/2 - 4t^3

A: Laplace transferom of the function

Q: find the inverse Laplace transform of the given function of 4e^(-2t) / (s(s+4))   Thank you for…

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Q: Solve equation using Laplace transform ÿ + 9y = 8 (t -) |sin(t), y(0) = 0, ý(0) = 0

A: Formulae:  1. Lf(t)δ(t-a)=e-asf(a) 2. Lf''(t)=s2F(s) - sf(0)-f'(0) 3. L-1e-asF(s)=H(t-a)f(t-a),…

Q: NO i need it to be the Fourier transform as X(jw). Dont use this as s tranfer functions  I dont…

A: Let us go through the subpart (b) whose integral to be evaluated is .The graph of the function with…

Q: Use convolution and Laplace transform to evaluate y''+y=sin(t) , y(0)=1 , y'(0)=-1

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Q: QI\ Find Fourier transform for: A) f(t) = U(t)sin² (3t) C) f(t) = elct sinh(bt)

A: (A)Given the function f(t)=u(t)sin2⁡(3t).Rewriting, .We know that, .The Fourier transform of f(t) is…

Q: Find the inverse Laplace transform f(t) = £¯¹ {F(s)} of the function F(s) = e −3s (1 – 4s) s² + 16

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Q: Find the Laplace transform F(s) = L{f(t)} of the function f(t) = 8th(t - 7), defined on the interval…

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Q: 2. ts) Use the table of Laplace Transforms and 1st shifting theorem to find the Laplace transform of…

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Q: Use the definition of the Laplace transform to find ℒ{f(t)} for f(t) = 2e^−3t Find the domain of the…

A: The explanation of the solution as follows:

Q: Find the convolution (f * g), after integrating find the Laplace transform of (f * g): f(t) = cos2t,…

A: We have to find convolution (f*g) and the Laplace transform of (f*g) wheref(t)= cos2t, g(t)= et .