y" + 4y = g(t) sin(t) if 0 _g(t) = { 0 y(0) = 1 y'(0) = 3 t≤2π if 2π t

Q: Q1 (a) Using the first shift theorem, find the following Laplace transform: L{e-2tcos3t)

A: The given question can be solved as shown in step2.

Q: Suppose solving an equation by Laplace transform results in Y(s) = s2 + 64' Evaluate y(7).

A: We have to solve given problem:

Q: 3y" + 6y + 3y = 9, y(0) = 0, /(0) = 6 %3D

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Q: Find inverse Fourier transform of F(W) %3D W2-2W+3

A: A complex domain function can be transformed into a real-time function through the inverse Fourier…

Q: i). ƒ (1) = (5– 312) ² i). ƒ (1) =r2sinh (21) Find the Laplace transforms of the following…

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Q: When I was considering what to do with my $10,000 lottery winnings, my broker suggested that I…

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Q: a) Find the Fourier transform of 4 f(t) = e tu(t) + -tu(t) + ²9.

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Q: Q2 \ Determine the Laplace transforms of the following function: t | e-4tt sin? 3t dt L

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Q: B: Find Laplace Transform of f(t)= cos3t By DEF.

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Q: L{7te-5t cosh(3t)+sin(√6t) — ²t³ + e=¹} -

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Q: Given y(t)=t²e+t. The above equation can be transform by using 1. First shift theorem 2. Second…

A: Given  y(t)= t2e4t

Q: 6. Find the inverse Laplace transform of the function (3²-²)(as + b) I(s) = (s² + a²) (s² + 3²)

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Q: Find the Laplace transform of the function f(t)= (5e/t+4t)using the table of known as2+bs+c…

A: We first find Laplace transform and then comparing we find the value of c.

Q: dt (te-¹u (t))?

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Q: Solve for the Laplace transform of f(t) = 5 using long method. %3D

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Q: g(t) = 8t4e5tu(-t)

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Q: So (sinh (-2t)e¯') u(t)

A: We shall find the Laplace transform of∫0tsinh-2te-tutdt that is L∫0tsinh-2te-tutdt First Shifting…

Q: Find the Laplace transform of f(t) = te-5t.

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Q: Find the Laplace Transform of L{e2t - sin(4t)}

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Q: Find the Laplace transform of  f(t)=-2u2(t)-3u3(t)+5u6(t)=......

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Q: Calculate the Laplace transform of the expression f(t) = sin tu(t – 2n) -

A: Given function: We have to calculate the Laplace transform of the given function.

Q: Please do the Fourier transform of the following formula u₁(xo, Yo) = exp(- exp(-xo+yo) wo

A: Given: u0x0,y0=exp-x02+y02w02 To find: Solution

Q: f(t) = [1– u2m(t)](2 sin t – sin 2t) U2n

A: Some of the properties of Laplace transformation Lsinat=as2+a2Luc(t)=e-cssLuc(t)g(t)=e-csL[g(t+c)]

Q: Solve using method of undetermined coefficients: y" + y' - 2y = x². %3D

A: Solution :-

Q: f(t) = [1– uzn(t)](2 sin t – sin 2t

A: Solution

Q: Determine the Laplace Transform of est cos 5t .

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Q: find the Laplace transform of t²cos(wt)

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Q: Determine the Laplace transform of the equation f (x) = 2e-"sin4t 16 A s2+ 4s + 20 20 B s2+ 4s + 20…

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Q: I have not yet been taught Laplace Transform by my lecturer, I believe. Isn't there another way…

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Q: What would the inverse Laplace Transform be for the attached function if A = 1+j4 and B = 3+j7?…

A: Step 1: Step 2: Step 3: Step 4:

Q: Q3: Find the solution of the Laplace transforms of the following functions: -3s2-12s-8] L-1 1)…

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Q: Find the Fourier transform $\tilde{f}(p)$ of the function 4x²e-5¹ for x ≥ 0 for x < 0. f(x) = {…

A: fx=4x2e-5xfor x≥00for x&lt;0

Q: Q1. a) Derive the Laplace transform of 3e4t from first principles (i.e. without using the list of…

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