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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
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A system has a complex conjugate root pair of multiplicity two or more...
Answer: c
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.
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.
Most Upvoted Answer
A system has a complex conjugate root pair of multiplicity two or more...
The impulse response of a system can provide valuable information about its behavior and stability. In this case, we are given that the system has a complex conjugate root pair of multiplicity two or more in its characteristic equation. Let's analyze the implications of this on the system's impulse response.
Complex Conjugate Root Pair
A complex conjugate root pair in the characteristic equation of a system indicates the presence of oscillatory behavior in the system's response. Complex conjugate roots are of the form a ± bi, where a and b are real numbers and i is the imaginary unit (√-1). These roots give rise to sinusoidal terms in the impulse response.
Multiplicity Two or More
The multiplicity of a root refers to the number of times it appears in the characteristic equation. When a complex conjugate root has a multiplicity of two or more, it means that it appears multiple times in the equation. This results in an exponential rise or decay in the sinusoidal terms of the impulse response.
Implications on the Impulse Response
Based on the given information, the impulse response of the system will exhibit the following characteristics:
1. Sinusoidal Oscillation: The presence of a complex conjugate root pair indicates the occurrence of sinusoidal terms in the impulse response. These sinusoids represent the oscillatory behavior of the system.
2. Exponential Rise: Since the complex conjugate root pair has a multiplicity of two or more, the sinusoidal terms in the impulse response will experience exponential rise. This means that the amplitude of the oscillation will increase over time.
3. Unstable System: An exponentially rising sinusoidal term indicates an unstable system. As the amplitude continuously grows, the system's response becomes unbounded and uncontrollable. This behavior is undesirable in most engineering applications.
Conclusion
In summary, a system with a complex conjugate root pair of multiplicity two or more in its characteristic equation will have an impulse response that exhibits a sinusoidal oscillation with exponential rise. This behavior indicates an unstable system, as the response grows without bound.
Complex Conjugate Root Pair
A complex conjugate root pair in the characteristic equation of a system indicates the presence of oscillatory behavior in the system's response. Complex conjugate roots are of the form a ± bi, where a and b are real numbers and i is the imaginary unit (√-1). These roots give rise to sinusoidal terms in the impulse response.
Multiplicity Two or More
The multiplicity of a root refers to the number of times it appears in the characteristic equation. When a complex conjugate root has a multiplicity of two or more, it means that it appears multiple times in the equation. This results in an exponential rise or decay in the sinusoidal terms of the impulse response.
Implications on the Impulse Response
Based on the given information, the impulse response of the system will exhibit the following characteristics:
1. Sinusoidal Oscillation: The presence of a complex conjugate root pair indicates the occurrence of sinusoidal terms in the impulse response. These sinusoids represent the oscillatory behavior of the system.
2. Exponential Rise: Since the complex conjugate root pair has a multiplicity of two or more, the sinusoidal terms in the impulse response will experience exponential rise. This means that the amplitude of the oscillation will increase over time.
3. Unstable System: An exponentially rising sinusoidal term indicates an unstable system. As the amplitude continuously grows, the system's response becomes unbounded and uncontrollable. This behavior is undesirable in most engineering applications.
Conclusion
In summary, a system with a complex conjugate root pair of multiplicity two or more in its characteristic equation will have an impulse response that exhibits a sinusoidal oscillation with exponential rise. This behavior indicates an unstable system, as the response grows without bound.
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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 stableb)A sinusoidal oscillation with a time multiplier ; the system is therefore unstablec)A sinusoidal oscillation which rises exponentially ; the system is therefore unstabled)A dc term harmonic oscillation the system therefore becomes limiting stableCorrect answer is option 'C'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about 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 stableb)A sinusoidal oscillation with a time multiplier ; the system is therefore unstablec)A sinusoidal oscillation which rises exponentially ; the system is therefore unstabled)A dc term harmonic oscillation the system therefore becomes limiting stableCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 stableb)A sinusoidal oscillation with a time multiplier ; the system is therefore unstablec)A sinusoidal oscillation which rises exponentially ; the system is therefore unstabled)A dc term harmonic oscillation the system therefore becomes limiting stableCorrect answer is option 'C'. Can you explain this answer?.
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 stableb)A sinusoidal oscillation with a time multiplier ; the system is therefore unstablec)A sinusoidal oscillation which rises exponentially ; the system is therefore unstabled)A dc term harmonic oscillation the system therefore becomes limiting stableCorrect answer is option 'C'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about 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 stableb)A sinusoidal oscillation with a time multiplier ; the system is therefore unstablec)A sinusoidal oscillation which rises exponentially ; the system is therefore unstabled)A dc term harmonic oscillation the system therefore becomes limiting stableCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 stableb)A sinusoidal oscillation with a time multiplier ; the system is therefore unstablec)A sinusoidal oscillation which rises exponentially ; the system is therefore unstabled)A dc term harmonic oscillation the system therefore becomes limiting stableCorrect answer is option 'C'. Can you explain this answer?.
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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 stableb)A sinusoidal oscillation with a time multiplier ; the system is therefore unstablec)A sinusoidal oscillation which rises exponentially ; the system is therefore unstabled)A dc term harmonic oscillation the system therefore becomes limiting stableCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for 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 stableb)A sinusoidal oscillation with a time multiplier ; the system is therefore unstablec)A sinusoidal oscillation which rises exponentially ; the system is therefore unstabled)A dc term harmonic oscillation the system therefore becomes limiting stableCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of 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 stableb)A sinusoidal oscillation with a time multiplier ; the system is therefore unstablec)A sinusoidal oscillation which rises exponentially ; the system is therefore unstabled)A dc term harmonic oscillation the system therefore becomes limiting stableCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice 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 stableb)A sinusoidal oscillation with a time multiplier ; the system is therefore unstablec)A sinusoidal oscillation which rises exponentially ; the system is therefore unstabled)A dc term harmonic oscillation the system therefore becomes limiting stableCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Electrical Engineering (EE) tests.
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