Determine the Laplace Transform of the following functions. 2 1. sin 3at where a is any positive constant and s > a. Problem 1. Which gives the Laplace transforms of the given time-domain function? Let a = 2 O pi - 2arctan (s/3) O pi - 2arctan (2s/3) pi - 2arctan (s/6) (1/2)pi - 2arctan (s/3)

Q: 5. f(t) = sin (6t).

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Q: Question 2. Find the inverse Laplace transform: 5 1 s-6

A: The formulas of Laplace inverse which will be used to obtain the solution of the given function are:…

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Q: 9. Show the Complex Fourier Integral Transform (Fourier transform) of the function defined below…

A: Given : The Complex Fourier Integral Transform (Fourier Transform) of the function is defined as :…

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

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Q: 5. Consider the following function: f(t)= Find the Laplace transform of this function. Lis odd -1 is…

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Q: Find and simplify the Laplace transform of the following functions, indicate the formula number from…

A: Formulas:Given the function .Consider .Differentiating, we getThis is essentially our function u(t).…

Q: 4s +4 (c) Find the inverse Laplace transform of Y(s) — ² + 4s +13) (d) Find the inverse Laplace…

A: The given problem is to find the Inverse Laplace transforms of the given functions Y(s).

Q: 6. Find the Laplace transform of the following functions (c) g(t) = cos 3tH(t-π)

A: Given function, gt=cos 3t Ht-π Ht-π is a Heaviside function defined by Ht-π=0if t<π1if t>π…

Q: 7. Find the inverse Laplace transform for the F(s): (S-2)e-2s 4s + 3 5² Hint: You may need unit step…

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Q: . Find Fourier cosine transform of - and deduce that 2. bx e 1 e V2m log р ға cos px dx

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Q: e the inverse Laplace transform of

A: The given function is ss2+2s+2  to find the inverse Laplace Transform proceed as follows rewrite the…

Q: The inverse transform of * 1 2 4s8s O % e (exp -t) sinh t O % e (exp t) sinh t O 1/4 e (exp -t) cosh…

A: Solution:  Given,  14s2-8s = 14(s2-2s)                             =14(s2-2s+1)-4=14((s-1)2-1) Now,…

Q: Determine the Laplace Transform of cos(2/3t) cos (V31) Note:

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Q: Find the laplace transform of cos at using the formula £{ƒ (t)} = est f (t) dt. Hencefind the…

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Q: Q3 Find Laplace transform of the function f (t)=t cos(@t)

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Q: s2 + 6s + 8 G(s) = s4 + 8s2 + 16° xnlanation calculation IS we

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

A: We have to find the Laplace Transform of the following function. 1)  f(t) = (2e-4t+sint)2

Q: Find the Fourier cosine transforms of 2e * 5e.2". 2.x

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Q: Find the inverse Laplace transform of the following function. F(s) = -³/+/

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Q: (a) Determine the Laplace transform of the following expression: te¹ sin 3t

A: To find the Laplace transform of the expression te-tsin 3t.  Using the Laplace formulae: Lsin…

Q: cos 4t-cos 2t 3. f(t) = t

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Q: Find the Inverse Fourier transform of Te-lw||

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Q: (A) Find Inverse Laplace transform for the following functions. 25+4 1.- 2.tan-¹) (5²+45+5)²

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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: For the Laplace transform, F (s) = +, find the time function (i.e. the inverse Laplace transform)…

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Q: Question #7. Use the Laplace transform to solve x"+x=2t, x(0) = 0, x'(0) = 5.

A: (.)   Given differential equation is ,          x''+x=2t   ;  x(0)=0  , x'(0)=5 (.) Some properties…

Q: Find Fourier Sine and Cosine transform of the function f(x) = e -x

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Q: Question 9 Calculate the average of the function g(x) = sin 3x over the interval [pi/2, pi] 5/pi a O…

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Q: a) f(t) = 2tOREM (0) c) f(t) = sint e) f(t) == {1 t, 1<t<∞

A: (.) Given function is,                   (.) Laplace transform:  Let  be a function of  defined for…

Q: Find the inverse Laplace transform following: 1. 2s+8 s²+4 4s+32 2. s²-16 3. 2S-1 s²-6s+18

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

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Q: Find the given inverse Laplace transform. 1 s² +45+5 a. e'sin(t) b. e-sin(t) c. e-icos(2t) d. e-…

A: The given inverse Laplace transform is .We have to find the inverse Laplace transform.