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 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
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.