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If the damping ratio is equal to 1, a second-order system is _________

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If the damping ratio is equal to 1, a second-order system is _________

(a) having maginary roots of the characteristic equation

(b) underdamped

(c) critically damped with unequal roots

(d) critically damped with equal roots

The question was posed to me in my homework.

My doubt is from Time Response of Control Systems in chapter Control System Applications of MATLAB

1 Answer

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Right option is (d) critically damped with equal roots

Explanation: The time response of a system with a damping ratio of 1 is critically damped. But the roots of the characteristic equation will be equal and equal to negative of the natural undamped frequency of the system.

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