d²0 de dt² dt +4- + 40 = 8. In a galvanometer, the deflection satisfies the differential equation do Use Laplace Transforms to solve the equation for 0, given that when t = 0, 0 = dt = 2.

Q: y Ct) = 5e - 2t Cos 67 fCt) = 3c 4t C1- 3t + 2t 2) -4t (1- 3t + 2t²)

A:

Q: 8s – 18 Find the inverse Laplace transformf(t) = L¯' {F(s)} of the function F(s) : s2 – 4s + 20

A: Consider the provided the question,

Q: Solve the Inverse Laplace Transform. Write your answer on clean paper clearly and readable. Don't…

A:

Q: 3.) f(t) = ½ (4-3) ² u(1-3)

A: Laplace transform of the function

Q: If L{f"(t)} = arctan ), f(0) = 2 and f'(0) = 1, find L{f(t)}. %3D

A: Given - If ℒf''t = arctan12 , f0 = 2 and f'0 = 1  To find - ℒft       Formula used - ℒfnt = snFs -…

Q: g(t) = 10rect [²(t+³)] ej²¹ 5 ej²nfot j2πfot

A: What is Fourier Transformation: A Fourier transform (FT) is a mathematical transformation that…

Q: 4. Find L'{ -}. Give table number. 3-5S

A: We have to find L-123-5swe are going to use the formulaL-11s-a=eat ——(*)

Q: 8. y" +9y = 20e y(0); y' ||

A:

Q: 51 3 2 LO

A: Z transform of the function

Q: t' Find L 10e-5t sin - 2.

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: 1 s²+4s+4

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Q: sin 3t f(t) t

A:

Q: 1. Solve: 2y' — y y (1) = es; y (0) = 2 ? Which of the following is within 0.01 of the right answer:…

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Q: Solve the inverse Laplace transform: 2s-4 s2+8s+13

A:

Q: 1-e g(t) t

A: Given the given function is gt=1-ett. Apply formula Lftt=∫s∞fsds L1=1sLeat=1s-a log a-log b=logab

Q: Let A = -127 0 -8 4 0 and 6- = 36 7 Define the linear transformation T: R2 → R³ by T(x) = Ar. Find a…

A:

Q: 3. Use definition (not tables) of L{f(t)}= [ e"f (t)dt to find L{1*e" } . Assume s>9

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Q: 3s+10 W (s) s(s-8)(s-6)²

A:

Q: 2ct-3) cos Cも-3) yct) = sin 2t cos 3t

A:

Q: Let g(t) be the function g(t) = Solve: 2t, ostco occe 127 12 y"+y = g(t), y(0) = 0, y'lol = 1.

A:

Q: L{e-3t-2e sin 3t} rmine the following transform.

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Q: Question 1.i.) A truncated sine wave { sin5x, -T <x <T y = f(x) = 0, otherwise

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Q: 2s2+10s F(s) (s + 1) s2-2s+5

A:

Q: -t cos(3t

A: To solve this problem, we  use the  result of laplace transformation.

Q: Solve the equation (2x + 6) (2y² + 3) dx + 4y(x² + 3x + 2) dy = 0

A:

Q: 2s – 10 -5s

A: We have to solve given problems:

Q: Using the definition, determine the transform of the function whose graph is

A: Given: To find: Transform of the function for the given graph.

Q: Transform * y = 3sinh (3t) 3 s² +9 3 s² - 9 OA) O B) Transform * s² + 1 S³ + s OA) OB) 1 - sint 9 s²…

A:

Q: -s-1 1. F(s) s2+s-2 2s+5 2. F(s) (s-3)2

A:

Q: 4iw i3w3 + 6i²w2 + 11iw + 6

A: Given: 4iωi3ω3+6i2ω2+11iω+6 To find: Inverse Fourier Transform of the given expression.

Q: y"" + 3y" +3y' + y = 0, y(0) = 7, y'(0) =-7, y"(0) = 11

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Q: 0 9. f(t)=t-n 0 if t 2π

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Q: Find F(2). 5sinh (3t) + 4cosh (3t) round off to 1 decimal place. Answer: -4.6

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Q: Sketch the following functions and find their Laplace Transforms: 1.) (t – 1)u(t – 1)

A: Image is attached with detailed solution.

Q: 2ィ 4= e そーを 4(t) dt

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: if t 5. t-5 ● i +7x = 4t, x(0) = 5 • ï + 14x + 58x = 174, x(0) = (0) = 0

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Q: a'(t) = -x(t – 1), x(t) = 1 on [-1,0], is given by 1(t) = E(-1)* t – (k – 1))* k! for n-1<t <n, k=0

A: As per the question we are given the following first order time varient differential equation :…

Q: 2s-1 's²-6s+18*

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Q: 2s + 16 s +4s + 13 S

A: If L[f(t)]=F(s), then f(t) is called the inverse Laplace transform of F(s). ie;

Q: %3D

A: