Question
Asked Dec 15, 2019
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Solve the following problem:

 

Determine the initial and final values of y(t) if its Laplace transform Y(s) is given by
10(2s +3)
Y(s)%3D
s(s2 +2s + 5)
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Determine the initial and final values of y(t) if its Laplace transform Y(s) is given by 10(2s +3) Y(s)%3D s(s2 +2s + 5)

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Expert Answer

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Step 1

According to the initial and final value theorem of Laplace transform, given a function Y(s), the initial and final value of the corresponding time domain function y(t) will be:

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Initial value:y(0) = lim sY(s) – –> (1) Final value:y(0) = lim sY(s) ––>(2)

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Step 2

In this case, the function Y(s) is given as

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10(2s +3) Y(s) =- s(s² + 2s +5) ---> (3)

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Step 3

So, using equation (1), the initial value of y(t) will be

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y(0) = limsY(s) 10(2s +3) = lim s s* s(s² + 2s +5) 10(2s +3) = lim- (s² + 2s +5) 3 10 = lim- 3 1+=+ 10 = lim- 3 1+-

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Electrical Engineering

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