[Solved] 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:

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Q.	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
Answer» C. a sinusoidal oscillation which rises exponentially ; the system is therefore unstable
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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