Question

A system has a complex conjugate root pair of multiplicity two or more in its characteristic equation. The impulse response of the system will be:

(a) A sinusoidal oscillation which decays exponentially; the system is therefore stable

(b) A sinusoidal oscillation with a time multiplier ; the system is therefore unstable

(c) A sinusoidal oscillation which rises exponentially ; the system is therefore unstable

(d) A dc term harmonic oscillation the system therefore becomes limiting stable

The question was asked by my college professor while I was bunking the class.

Origin of the question is Time Response of Second Order Systems topic in chapter Time Response Analysis, Design Specifications and Performance Indices of Control Systems

Answer 1

The correct answer is (c) A sinusoidal oscillation which rises exponentially ; the system is therefore unstable

For explanation: Poles are the roots of the denominator of the transfer function and on imaginary axis makes the system stable but multiple poles makes the system unstable.