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The Routh-Hurwitz criterion cannot be applied when the characteristic equation of the system contains any coefficients which is :
- a)Negative real and exponential function
- b)Negative real, both exponential and sinusoidal function of s
- c)Both exponential and sinusoidal function of s
- d)Complex, both exponential and sinusoidal function of s
Correct answer is option 'B'. Can you explain this answer?
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The Routh-Hurwitz criterion cannot be applied when the characteristic ...
Explanation: The Routh-Hurwitz criterion cannot be applied when the characteristic equation of the system contains any coefficients which is negative real, both exponential and sinusoidal function of s.
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The Routh-Hurwitz criterion cannot be applied when the characteristic ...
Explanation:
The Routh-Hurwitz criterion is a mathematical method used to determine the stability of a linear time-invariant (LTI) system by examining the coefficients of its characteristic equation. The characteristic equation is obtained by setting the denominator of the transfer function equal to zero.
The Routh-Hurwitz criterion is based on the fact that the stability of a system can be determined by analyzing the signs of the coefficients of the characteristic equation. However, there are certain cases where the Routh-Hurwitz criterion cannot be applied. One such case is when the characteristic equation contains coefficients that are negative real, exponential, and sinusoidal functions of 's'.
Reason:
The Routh-Hurwitz criterion is based on the assumption that the coefficients of the characteristic equation are real numbers. However, when the characteristic equation contains coefficients that are negative real, exponential, and sinusoidal functions of 's', it violates this assumption and the Routh-Hurwitz criterion cannot be directly applied.
Explanation of Option B:
Option B states that the Routh-Hurwitz criterion cannot be applied when the characteristic equation contains coefficients that are negative real, exponential, and sinusoidal functions of 's'. This option is correct because the Routh-Hurwitz criterion is not applicable in such cases due to the violation of the assumption that the coefficients are real numbers.
Example:
Let's consider an example to illustrate this. Suppose we have a characteristic equation given by:
s^2 + (3e^(-s) - sin(s))s + 2 = 0
In this equation, the coefficient of 's' is a combination of a negative real number (3e^(-s)) and a sinusoidal function (-sin(s)). Since the coefficient is not a real number, the Routh-Hurwitz criterion cannot be applied.
Conclusion:
In conclusion, the Routh-Hurwitz criterion cannot be applied when the characteristic equation of the system contains coefficients that are negative real, exponential, and sinusoidal functions of 's'. This is because the Routh-Hurwitz criterion is based on the assumption that the coefficients are real numbers.
The Routh-Hurwitz criterion is a mathematical method used to determine the stability of a linear time-invariant (LTI) system by examining the coefficients of its characteristic equation. The characteristic equation is obtained by setting the denominator of the transfer function equal to zero.
The Routh-Hurwitz criterion is based on the fact that the stability of a system can be determined by analyzing the signs of the coefficients of the characteristic equation. However, there are certain cases where the Routh-Hurwitz criterion cannot be applied. One such case is when the characteristic equation contains coefficients that are negative real, exponential, and sinusoidal functions of 's'.
Reason:
The Routh-Hurwitz criterion is based on the assumption that the coefficients of the characteristic equation are real numbers. However, when the characteristic equation contains coefficients that are negative real, exponential, and sinusoidal functions of 's', it violates this assumption and the Routh-Hurwitz criterion cannot be directly applied.
Explanation of Option B:
Option B states that the Routh-Hurwitz criterion cannot be applied when the characteristic equation contains coefficients that are negative real, exponential, and sinusoidal functions of 's'. This option is correct because the Routh-Hurwitz criterion is not applicable in such cases due to the violation of the assumption that the coefficients are real numbers.
Example:
Let's consider an example to illustrate this. Suppose we have a characteristic equation given by:
s^2 + (3e^(-s) - sin(s))s + 2 = 0
In this equation, the coefficient of 's' is a combination of a negative real number (3e^(-s)) and a sinusoidal function (-sin(s)). Since the coefficient is not a real number, the Routh-Hurwitz criterion cannot be applied.
Conclusion:
In conclusion, the Routh-Hurwitz criterion cannot be applied when the characteristic equation of the system contains coefficients that are negative real, exponential, and sinusoidal functions of 's'. This is because the Routh-Hurwitz criterion is based on the assumption that the coefficients are real numbers.
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The Routh-Hurwitz criterion cannot be applied when the characteristic equation of the system contains any coefficients which is :a)Negative real and exponential functionb)Negative real, both exponential and sinusoidal function of sc)Both exponential and sinusoidal function of sd)Complex, both exponential and sinusoidal function of sCorrect answer is option 'B'. Can you explain this answer?
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The Routh-Hurwitz criterion cannot be applied when the characteristic equation of the system contains any coefficients which is :a)Negative real and exponential functionb)Negative real, both exponential and sinusoidal function of sc)Both exponential and sinusoidal function of sd)Complex, both exponential and sinusoidal function of sCorrect answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The Routh-Hurwitz criterion cannot be applied when the characteristic equation of the system contains any coefficients which is :a)Negative real and exponential functionb)Negative real, both exponential and sinusoidal function of sc)Both exponential and sinusoidal function of sd)Complex, both exponential and sinusoidal function of sCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The Routh-Hurwitz criterion cannot be applied when the characteristic equation of the system contains any coefficients which is :a)Negative real and exponential functionb)Negative real, both exponential and sinusoidal function of sc)Both exponential and sinusoidal function of sd)Complex, both exponential and sinusoidal function of sCorrect answer is option 'B'. Can you explain this answer?.
The Routh-Hurwitz criterion cannot be applied when the characteristic equation of the system contains any coefficients which is :a)Negative real and exponential functionb)Negative real, both exponential and sinusoidal function of sc)Both exponential and sinusoidal function of sd)Complex, both exponential and sinusoidal function of sCorrect answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The Routh-Hurwitz criterion cannot be applied when the characteristic equation of the system contains any coefficients which is :a)Negative real and exponential functionb)Negative real, both exponential and sinusoidal function of sc)Both exponential and sinusoidal function of sd)Complex, both exponential and sinusoidal function of sCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The Routh-Hurwitz criterion cannot be applied when the characteristic equation of the system contains any coefficients which is :a)Negative real and exponential functionb)Negative real, both exponential and sinusoidal function of sc)Both exponential and sinusoidal function of sd)Complex, both exponential and sinusoidal function of sCorrect answer is option 'B'. Can you explain this answer?.
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