Correct Answer - Option 1 : 0
Concept:
Final value theorem:
A final value theorem allows the time domain behavior to be directly calculated by taking a limit of a frequency domain expression
The final value theorem states that the final value of a system can be calculated by
\(x\left( \infty \right) = \mathop {\lim }\limits_{s \to 0} sX\left( s \right)\)
Where X(s) is the Laplace transform of the function.
NOTE:
- For the final value theorem to be applicable system should be stable in a steady-state and for that real part of the poles should lie on the left side of the s plane.
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In the given problem exactly the final value theorem is not applied but just X(0+) is calculated.
Calculation:
Given that,
\(X(s) = \frac{{3{s^2} + 5s}}{{{s^2} + 10s + 21}}\)
It is asked to calculate X(0+) which is the value of Laplace transform at s = 0+
\(x\left( \infty \right) = X\left( 0 \right) = \mathop {\lim }\limits_{s \to 0} sX\left( s \right)=\frac{{3{\times0^2} + 5\times0}}{{{0^2} + 10\times0 + 21}} = 0\)
