4 The Laplace transform of f (t) = {*. 0st<2 is: t2 2

Q: = Find the inverse Laplace transform f(t) = L-¹ {F(s)} of the function F(s) = f(t)= [38+4 +36 = L-1,…

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Q: Find the inverse Laplace transform L-1{F(s)} of the given function. 4 F(s) = s2 + 4 Your answer…

A: Given,           Fs=4s2+4

Q: Ex. Find the Laplace transform for the functions 1-f (t) = sin't %3D 2-f (t) =t°e"

A: We have to use Laplace standard transformations.

Q: Q1\ Find the Laplace transform for the following function: f(t) = - 24 t5/2 + t e3t sin (6t)

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Q: solve y(4)-3y'''+2y''=e3x  using undetermined coefficient

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Q: 5s + 20 F(s) = s2 + 8s + 97

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Q: Find the sine transform of a function of x which is equal to sin x for 0 <x<a and 0 for x2a.

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Q: f(t) = SO if 0 c where c> 0.

A: We have to solve given problem:

Q: Derive the Fourier transform for f(t) = te2t for t>0 and 0 for t<0.

A: The Fourier transform of the function f(t) is represented as F(k), it is defined as ∫-∞∞e-iktf(t)dt,…

Q: f(t) = when 0 k

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Q: Find the inverse Laplace transform of 7s + 3 82 + 17 8 >0

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Q: Evaluate the Laplace transform of f(1) = { ; 0≤t <% cost ; t≥% 0

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Q: x(t)=sin(t-3T)

A: Z transform

Q: when 0 k

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Q: Show that the finite sine transform of , 0 < x < n is (- 1y*'- p

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Q: 8 Find the inverse Laplace transform of F (s) = f (t) = 8"H(t) (Write eab as exp(a*b)). %3| ||

A: We have to find laplace inverse of F(s)

Q: Evaluate L{t sin kt} (Use the Derivatives of Transform)

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Q: B- Find Inverse Laplace transform of the following functions F(s)= 2s-7 (s+ 6)(s² + 4) G(s) = s(s² +…

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Q: Use the definition of the Laplace transform to find ℒ{f(t)} for f(t) = 2e^−3t Find the domain of the…

A: The explanation of the solution as follows:

Q: Q6/ Find the Inverse Laplace Transform 1 2- L-1 (s²+9).

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Q: (b) f (x) = {sent, .if 0<t<n l0, if

A: We find Laplace transform of given function

Q: Q3\Find the Laplace transform of f(t) defined as 03

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Q: Find the Fourier Sine Transform of the function   if a = 7,  b = 7 , m = 5 , and n = 4. Then,…

A: The formula for the Fourier Sine Transform is :-  f^a=2π∫0∞fxsinaxdx   And we are given the function…