Solve the following initial value problem using Laplace transform: d²y dt² 19 dy where - dy +60y = g(t), y (0) = -1/2, t-o= 11, 2 0≤t <3 6 3 ≤t g (t) Let Y (s) be the Laplace transform of the solution y(t). Then evaluate Y(-1/2) y(-1/2). Y(-1/2) y (-1/2) =

Q: Find Laplace transform of x(t)=t (cos)^2 (wt)u(-2t). *

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Q: dy = et. dt Find the solution when y(0)=2 using the method of Laplace transform

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Q: When calculing the Laplace transform of the function f(t)=e^2t.sin(4t) is obtained as a result:

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Q: c) Use a pair (table) to findz-transform of x(n) = 20.65 √2 cos((-)n-1.415)u(n)

A: Introduction: There are many properties that are followed by Z-transformation. It helps us to…

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

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Q: Solve using Laplace Transform f(t) = (d2/dt2)(te-t)

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Q: . Find the Laplace transform of the function f(t) = 2t + 3 cos(3t) + 4 sin(3t)

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Q: Equation: Answer:

A: We want to find value of x. For this we use Pythagoras theorem, which states that Hypotenuse2 =…

Q: Find the inverse Laplace transform of -6s e F(s) = s2 + 2s – 3 - - (Use for u.(t) .)

A: The given expression is Fs=e-6ss2+2s-3. We have to find the inverse Laplace transform of function…

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

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Q: sin 2t (i) Find the Laplace transform of

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Q: Use Laplace transform to solve the following IVP y′′(t) = 4y(t) −e^(−t)U(t −1), y(0) = y′(0) = 0.

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Q: Let x(t)=5sinc(1.5t) +6cos(7/2) and h(t)=4sind(). Determine y(t)=x(t)*h(t) using Fourier Transform…

A: Let  and We need to determine y(t)=x(t)∗h(t).To solve this problem, we list the Fourier transforms…

Q: Determine the Fourier transform of f(t) = te-2t u(t), where

A: Given ft = te-2tut where ut =0     t&lt;01    t&gt;0 The Fourier transformation is given by Fw…

Q: If x has a value of -4, determine if the series converges (absolutely or conditionally) or…

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Q: d2y/dt2+a2y=b sin wt  ( laplace transform )

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Q: y (t) = 1- y(t-r)e e*dr , y(0) = 1 -2r

A: To solve the below equation using the Laplace transform. y't=1−∫0tyt−τe−2τdτ, y0=1

Q: Find the Fourier transform of f(t) = {, t 0 12e-t O 2/(1+jw) O 1/(1+jw) O -1(1+jw) O -2/(1+jw)

A: We have to find the Fourier transform.

Q: (t², 0st<2 Find the Laplace transform of F(t) - 5, t2 2

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Q: 7. Use the Laplace transform to solve the difference equation 3x (t) 4x(t-1) = 1, x(t)=0 for t < 0.…

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Q: ý + 16y = 8 (t – ) sin (2t), y(0) = 0, ÿ(0) = 0

A: The solution is given by using some formulas of Laplace transform as follows :

Q: 1. Find the forier tansform of f(t) = 8(t) + 2e-3lt| %3D

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Example Find the Fourier transform of the rectangular pulse duration T and amplitude A T T SC) = 4…

A: The given problem is to find the Fourier transform for the given rectangular pulse function.

Q: orm y(t) = 4e-2cos

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Q: Use (8), • S* f(1) dt = £^¹{F(5)}, to evaluate the given inverse transform. (Write your answer as a…

A: we know that laplace transform of e^(at) is (1/(s-a)).

Q: Find Z transform for 3 F(t) = t * * F(t) = u(t-2)

A: Given that F(t)=t3 F(t)=u(t-2) We have to find the Z transformation of f(t).