Evaluate the Laplace Transform of the given function using appropriate theorems. S(t) = t2 + 3 t°. f(t) = t2 + 3t + 13/2. f(t) = t e-3t + e!. f(t) = t? cos 2t. %3D f(t) = cos t sin t. f(t) = t sinh 3t. %3D f(t) = et+1 cos t. %3D f(t) = eat43/2 f(t) = eat cos Bt. %3D

Q: a) Consider the following function f(t): cos 2t, 1() = { cos t, TM i. Express the function in terms…

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Q: Note: Review your trigonometric ident 1. f(t) = 5sin2t - 6cost 2. f(t) = 3sintcost

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Q: Find the Laplace transform of: 1. f(t) = e(-3t) sin(2t) cos(3t) cosh(t)

A: Given that 1) f(t) = e-3tsin (2t) cos (3t) cosh (t) 2) f(t) = 1+sin t + (8t)15 + t2cos 3t We have to…

Q: Q.5A/Find Laplace Transform of the following functions 1.f(t) = 6e-6t + +5t3-9 2./(t) = (42marke)…

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Q: Q1: A: Find the Laplace Transformer for the following function [8 sin²t cos²t] t L

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Q: sin 3t f(t) t

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Q: Find the Laplace transform of the following: 2. f(t) = v1+ sin t + (5t)18 + t² cos 2t

A: Here given function as ft=1+sin t+5t18+t2cos 2torft=sin2t2+cos2t2+2sin t2cost2+5t18+t2cos…

Q: Use the step function to calculate the transforms of the functions below. Evaluate at s = 1.

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Q: Find the Laplace transform F(s), given that f(t) is: (a) 2tu(t – 4) (b) 5 cos(t) 8(t – 2)

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Q: 3) Find the Laplace transform of h(t) = etv sin v du.

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Q: L{te-2tcos?t} Find the Laplace transform of the function?

A: Given the given expression is Lte-2tcos2t Apply formula Ltn=n!sn+1Leattn=n!s-an+1…

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Q: Apply Fourier transform, jw F(w) = F₁ (w) + F₂ (w)...... equation 2 |F₁(t) = −8(t + 2) +…

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Q: 3. f(t) = cosh(3t) %3D

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Q: Find the Laplace Transform of the following functions: 1. f(t) = (2e-4t + sin t)²

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Q: Find the Inverse Laplace Transform of s?+2s + 10 'sin3t A 3 3 sin9 3. cost

A: Inverse Laplace transferom

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Q: Note:M=13 1. Find the Laplace transform of the function: f (t) = eMCosh(Mt) – Msin³ (t) + M sin(Mt)…

A: given function ft=eMt CoshMt-Msin3t+M sinMtcost here  M=13 thus, ft=e13t Cosh13t-13sin3t+13…

Q: 2. Find the Laplace transform of the following functions. (Use the table.) (a) g(t) = 2e“ + 21²e“

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Q: sen(22t) 0<t <- f(t) = cos(12t) t25

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Q: Show the following Fourier Transform and F{tri(t)}(f) = sinc²(f) F{e-t²}(f) = e-f² You may use the…

A: Given: Here is the given Fourier Transforms,  Ftritf=sinc2f and  Fe-πt2f=e-πf2

Q: 16. t cos 4t 18. cos2 2t

A: according to our guidelines we can answer only three subparts, or first question and rest can be…