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 stableThe 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

A system has a complex conjugate root pair of multiplicity two or more

1.	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 stableThe 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» 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.

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