Question

The final value theorem is used to find the

• A. steady state value of the system output
• B. initial value of the system output
• C. transient behavior of the system output
• D. none of these

Hint:

Final value theorem gives information about system behavior as time approaches infinity.

Answer 1

The Correct Option is A

Step 1: Understanding final value theorem.
The final value theorem is a concept from Laplace transform used to determine the long-term behavior of a system. It helps find the value of the system output as time approaches infinity.
Step 2: Mathematical expression.
If $Y(s)$ is the Laplace transform of $y(t)$, then the final value theorem states:
\[ \lim_{t \to \infty} y(t) = \lim_{s \to 0} sY(s) \] provided all poles of $sY(s)$ lie in the left half of the $s$-plane.
Step 3: Eliminating incorrect options.
Initial value is obtained using the initial value theorem, not the final value theorem.
Transient behavior refers to short-term response, not steady state.
Step 4: Final conclusion.
Hence, the final value theorem is used to determine the steady state value of the system output.