Problem 4. Solve the following IVP using a Laplace transform, wher 8(t) is the Dirac delta function. y″(t) + y(t) = 1 + 8(t − 2π) when y(0) = 1, y'(0) = 1 Make sure to follow the following outline, and box these intermediate points along the way: • Finding the appropriate transformation of the ODE using the Laplace transform. ⚫ Solving the resulting equation for Y(s) = &{y(t)} Taking the inverse Laplace transformation to find y(t). • Writing your final answer as a piecewise function (that is, without the unit step function). • Graphing your solution (using Desmos).

Q: 1- 3s Find the Inverse Laplace Transform of G (s) =- s2+ 8s +21 13 8 (1) = – 3e -d"cosh(V51) +…

A: Given Gs=1-3ss2+8s+21 to find the inverse Laplace transform Solution:-

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Q: 17. y"-5y6y=t² + 7, y(0) = 1, y'(0) = 0

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Q: 6(5 – 5) (s - 5)2 +. Laplace Transform of 6e cos (2t):

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Q: Problem 1: (7 points) For following function, do the following: (i) Write the function as a…

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Q: 2. Find the inverse transforms of the following. Show details of your work a. (s+10)/(s² - s - 2) b.…

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Q: If F(w) is the Fourier transform of f(t), then the Fourier transform of g(t) = -5e²jt f(t) may be…

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Q: x' (t) + 4x' (t) = −2t – sin(t – 4), with x(4) = 0, and x'(4) = 1.

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Q: Problem B-2-3 Obtain the Laplace transform of the function defined by f(t) = 0 t < 0 t≥ 0 = 1²e-at

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Q: Question 22 6s – 5 Find the Inverse Laplace Transform of F (s) = s2+7 5 A f (1) = 6cos(/7t ) -…

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Q: Determine the Fourier Transform of the following function. -2 <x < 0, 0 <x < 2; Problem 1: f(x) =…

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Q: x' (t) + 5x'(t) + 6x(t) = e−²(t−¹), with x(1) = 0, and x′(1) = 0.

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Q: problem: Solve the following equation using the toplace transform. 2² w 2 z²w дяг a t² I sint с ₂ W…

A: Introduction: An initial boundary value problem (IBVP) is said to be properly stated mathematically…

Q: 1. Find the inverse Laplace transform y(t)=L−¹[Y(s)] where (b) Y(s)-e-³s (25-3) $²-49

A: We will be using the formulas of inverse Laplace L-1{a·fs+b·gs}=a·L-1{fs}+b·L-1{gs} L-1{1s-a}=eat…

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A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

Q: Consider the following continuous time signal y(t) given by y(t) = 6 p4(t – to) + 10 pr(t – 2)…

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Q: 1. f(t) = e-3t-2| %3D

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Q: Question 1: Compute the Fourier transform follows: a) f (t) = -5?u(t)e-st +e=7t=

A: Given,                     f(t)=-1t-52u(t)e-5t+e-7t2Where u(t) is the unit step function.

Q: Given that y(0) = 4 which of the following is the Laplace Transform of the expression y' - y? Here…

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Q: Question 7 2s +3 Find the Inverse Laplace Transform of F (s) = s2+4s + 13 A f(t 2sin3t--cos3t 3…

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Q: 1 The inverse Laplace transform: a{, is: Is²– 36) - (A) 6sin(61 ) (B) -cosh(6t) 1 -sinh(6t) (D) None

A: It is given    Gs=1s2-36=1s2-62         =1·66s2-62=16·6s2-62   The inverse transform is then…

Q: Question 2. Express the function f(t) = in terms of unit step functions and hence determine F(s),…

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Q: Consider the equation v (1) – 2 = -13 / vu)du (0) = 10 | erforming the process to solve the given…

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Q: Find the Laplace Transform of the following function. 10e-5t sin 2.

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Q: QUESTION 1. Find the Laplace transform of the following functions. Here, represents con volution. a)…

A: Find the Laplace transform of the functions. a) t2e-2tsin2t b) u2tt2-4t+3 Here we the formulas:…

Q: Suppose that f is a infintely-differentiable function whose Laplace transform exists, with f(0) = 2,…

A: Question - 4 Given, f0=2f'0=-3f''0=5 Lfx=1ω2+1gω=Lf'''x

Q: If the Fourier transform of f(t) = { √3 2<t<4 0 elsewhere is F(w), express the Fourier transform of…

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Q: Compute the Laplace Transform of the given functions: First, rewrite in terms of step functions! To…

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Q: A rental truck costs $45.45 for a day plus 94¢ per mile. (a) If x is the number of miles driven,…

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Q: Find the inverse Laplace transform £¹{F(s)} of the function F'(s) = 10 (s-4)³ NOTE: The answer…

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Q: Question 8. 3s2 If F(s) = -s+1 is the Laplace transform of f(t), find the following, correct to…

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Q: Consider the initial value problem dy d²y dy dt2 dt +10. +41y=-7e5t cos(5t), y(0) = -7, ,dt -(0) -4…

A: Step 1:  Y(s) Partial Fractions:The equation can be rewritten to isolate Y(s): (s2 + 10s + 41) Y(s)…

Q: Question 3. If F(w) is the Fourier transform of f(t), then the Fourier transform of g(t) = 2e5jt…

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Q: " when y(0) = -1 t > // Problem 3. Solve the following IVP using a Laplace transform. (2 cos(t), t</…

A: Step 1: Step 2: Step 3: Step 4:

Q: Question 8 Find the Laplace transform of h(t) = 3sinh(2t) + 3sin (2t) 3 (A H(s) + s2+4 s2- 4 2 В…

A: Laplace transferom