The final value theorem, used to find the steady-state output x_o(infty) from the Laplace transform X_o(s), states:

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Mechanical Engineering QUESTION #2392

Question 1

The final value theorem, used to find the steady-state output \(x_o(\infty)\) from the Laplace transform \(X_o(s)\), states:

\(x_o(\infty) = \lim_{s\to\infty} s X_o(s)\)
\(x_o(\infty) = \lim_{s\to 0} s X_o(s)\)✔️
\(x_o(\infty) = \lim_{s\to 0} X_o(s)\)
\(x_o(\infty) = \lim_{s\to\infty} X_o(s)\)

Correct Answer Explanation

Final value theorem: \(x_o(\infty)=\lim_{t\to\infty}x_o(t)=\lim_{s\to0}sX_o(s)\). Valid when all poles of \(sX_o(s)\) are in the left-half s-plane. Used to find steady-state error without inverting the Laplace transform.

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