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An underdamped second order system with negative damping will have the roots :
- a)On the negative real axis as roots
- b)On the left hand side of complex plane as complex roots
- c)On the right hand side of complex plane as complex conjugates
- d)On the positive real axis as real roots
Correct answer is option 'C'. Can you explain this answer?
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An underdamped second order system with negative damping will have the...
Answer: c
Explanation: An underdamped second order system is the system which has damping factor less than unity and with negative damping will have the roots on the right hand side of complex plane as complex conjugates.
Explanation: An underdamped second order system is the system which has damping factor less than unity and with negative damping will have the roots on the right hand side of complex plane as complex conjugates.
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An underdamped second order system with negative damping will have the...
Underdamped Second Order System with Negative Damping
An underdamped second order system is characterized by having two complex conjugate roots in its characteristic equation. The damping ratio, denoted by ζ, determines the behavior of the system. When ζ is less than 1, the system is said to be underdamped.
Negative damping means that the damping coefficient is negative. This implies that the system is being driven, rather than being damped. In such a case, the roots of the characteristic equation will be given by:
s = -ζωn ± jωn√(1-ζ²)
where ωn is the natural frequency of the system.
Roots on the Right Hand Side of Complex Plane
When the damping ratio is less than 1 and the damping coefficient is negative, the roots of the characteristic equation will be complex conjugates with a positive real part. This means that the roots will lie on the right hand side of the complex plane.
This behavior is due to the fact that negative damping causes the system to oscillate with increasing amplitude. As a result, the system becomes unstable and the roots move to the right hand side of the complex plane.
Conclusion
In conclusion, an underdamped second order system with negative damping will have roots on the right hand side of the complex plane as complex conjugates. This behavior is due to the fact that negative damping causes the system to become unstable and oscillate with increasing amplitude.
An underdamped second order system is characterized by having two complex conjugate roots in its characteristic equation. The damping ratio, denoted by ζ, determines the behavior of the system. When ζ is less than 1, the system is said to be underdamped.
Negative damping means that the damping coefficient is negative. This implies that the system is being driven, rather than being damped. In such a case, the roots of the characteristic equation will be given by:
s = -ζωn ± jωn√(1-ζ²)
where ωn is the natural frequency of the system.
Roots on the Right Hand Side of Complex Plane
When the damping ratio is less than 1 and the damping coefficient is negative, the roots of the characteristic equation will be complex conjugates with a positive real part. This means that the roots will lie on the right hand side of the complex plane.
This behavior is due to the fact that negative damping causes the system to oscillate with increasing amplitude. As a result, the system becomes unstable and the roots move to the right hand side of the complex plane.
Conclusion
In conclusion, an underdamped second order system with negative damping will have roots on the right hand side of the complex plane as complex conjugates. This behavior is due to the fact that negative damping causes the system to become unstable and oscillate with increasing amplitude.
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An underdamped second order system with negative damping will have the roots :a)On the negative real axis as rootsb)On the left hand side of complex plane as complex rootsc)On the right hand side of complex plane as complex conjugatesd)On the positive real axis as real rootsCorrect answer is option 'C'. Can you explain this answer?
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