L[u(t)] = F(s) = Q1/ What is the relationship between Laplace transform u(t)dt -st e and the following transform E[u(t)] = T(w) = = W ew u(t)dt Some Properties:- 1. E[1] = w² 2. E[t] = w3 3. Elex]= 1-aw

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: Find the inverse Laplace transform of the function as + b H(s) = (s – a)2 + 32 °

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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: What is the inverse Laplace Transform of this function if one term is 1/s and the other is 1/s+a?

A: The inverse Laplace transform of F(s) is f(t) = 3 + 4e^-2t - 7e^-5t

Q: The Laplace transform of x(t) is X(s). Given x(0)=2 and x'(0)=-1, write an expression for the…

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Q: Find the inverse Laplace transform L-{F(s)} of the function e-2s F(s) : %D s2 + 5s – 50 NOTE:…

A: Given that Fs=e-2ss2+5s-50 We have to find the inverse Laplace transform of Fs that is L-1Fs For…

Q: = Find the inverse Laplace transform f(t) = £¹{F(s)} of the function F(s) = f(t) = = L 6s+2 s² + 100…

A: The function: Fs=6s+2s2+100. We have to find the inverse Laplace transform of the given function.

Q: Find the inverse Laplace transform f(t) = L¹{F(s)} of the function F(s) = = f(t) = L -- {7+5)-1…

A: Solution:-

Q: 5. Find the inverse Laplace transform of the function H(s) = as + b (s-a)² +32° a = 9,b= 10, a = 4,8…

A: We have to find the inverse Laplace transform of the function H(t)=as+b(s-α)2+β2 when a=9, b=10,…

Q: y -7y +10y= 9cost+7sint, 5, y =-4 2

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Q: Find the inverse Laplace transform f(t) = L-' {F(s)} of the functic 5 3s F(s) = s2 + 16 s2 + 49 } 5…

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