Home › MCQs › Mechanical Engineering › Question #2384
Back to Questions
Mechanical Engineering QUESTION #2384
Question 1
The Routh-Hurwitz criterion for stability of a system with characteristic equation \(D(s)=a_n s^n + a_{n-1}s^{n-1}+\cdots+a_0=0\) states:
  • All coefficients must be positive AND all elements in the first column of the Routh array must have the same sign✔️
  • Only the first and last coefficients must be positive
  • The determinant of the coefficient matrix must be positive
  • All coefficients must be equal
Correct Answer Explanation
Routh-Hurwitz criterion: (1) necessary condition: all coefficients \(a_i>0\); (2) necessary and sufficient condition: all elements of the first column of the Routh array must be nonzero and have the same sign. The number of sign changes equals the number of poles in the right-half plane.