Question:
The characteristic polynomial of a system is
\[
s^3+2s^2+4s+K.
\]
The system is marginally stable for
The characteristic polynomial of a system is
\[
s^3+2s^2+4s+K.
\]
The system is marginally stable for
Show Hint
For marginal stability using Routh criterion, look for a complete zero row or a first-column element becoming zero.
Updated On: Jun 25, 2026
- \(K=0\)
- \(K=8\)
- \(0<K<4\)
- \(0<K<8\)
Show Solution
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The Correct Option is B
Solution and Explanation
Concept:
Marginal stability can be determined using the Routh-Hurwitz criterion.
Step 1: Form the Routh array.
For \[ s^3+2s^2+4s+K=0, \] the Routh array is \[ \begin{array}{c|cc} s^3 & 1 & 4 \\ s^2 & 2 & K \\ s^1 & \frac{8-K}{2} & 0 \\ s^0 & K & \end{array} \]
Step 2: Apply marginal stability condition.
For marginal stability, a row becomes zero. Thus, \[ \frac{8-K}{2}=0. \] \[ 8-K=0. \] \[ K=8. \]
Step 3: Final answer.
\[ \boxed{K=8} \] Hence, \[ \boxed{\text{Correct Option (B)}} \]
Step 1: Form the Routh array.
For \[ s^3+2s^2+4s+K=0, \] the Routh array is \[ \begin{array}{c|cc} s^3 & 1 & 4 \\ s^2 & 2 & K \\ s^1 & \frac{8-K}{2} & 0 \\ s^0 & K & \end{array} \]
Step 2: Apply marginal stability condition.
For marginal stability, a row becomes zero. Thus, \[ \frac{8-K}{2}=0. \] \[ 8-K=0. \] \[ K=8. \]
Step 3: Final answer.
\[ \boxed{K=8} \] Hence, \[ \boxed{\text{Correct Option (B)}} \]
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