Question

The characteristic equation of a system is given by, \[ s^5 + 10s^3 + 5s^2 + 2 = 0 \] This system is:

• A. Stable
• B. Marginally Stable
• C. Unstable
• D. Absolutely Stable

Hint:

A system is unstable if the characteristic equation has roots with positive real parts, indicating that the system's response grows without bound.

Answer 1

The Correct Option is C

To determine the stability of the system, we check the characteristic equation's roots. If any roots of the characteristic equation have positive real parts, the system is unstable. In this case, the presence of terms without corresponding positive powers of \(s\) suggests that the system will have poles with positive real parts, indicating instability. Thus, the system is Unstable.