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The current response of a network to a unit step input is Io(s) = 10(s + 2)/s(s2 + 11s + 30). The response is
- a)Under damped
- b)Over damped
- c)Critically damped
- d)None of the mentioned
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The current response of a network to a unit step input is Io(s) = 10(s...
The roots are real and unequal (-6, -5) for the characteristic equation. Hence it is over damped.
Most Upvoted Answer
The current response of a network to a unit step input is Io(s) = 10(s...
Given: The response of the network to a unit step input is Io(s) = 10(s^2)/(s(s^2 - 11s + 30))
To determine the type of response, we need to analyze the denominator of the transfer function.
1. Find the roots of the denominator:
The roots of the denominator can be found by solving the quadratic equation s^2 - 11s + 30 = 0. The roots are s = 6 and s = 5.
2. Classify the response based on the roots:
The type of response is determined by the nature of the roots. In this case, we have two distinct real roots: s = 6 and s = 5.
a) Underdamped response:
An underdamped response occurs when the roots are complex conjugates with a non-zero imaginary part. Since the roots in this case are real, the response cannot be underdamped.
b) Overdamped response:
An overdamped response occurs when the roots are real and distinct. In this case, the roots are distinct (s = 6 and s = 5), indicating an overdamped response.
c) Critically damped response:
A critically damped response occurs when the roots are real and repeated. Since the roots in this case are distinct, the response cannot be critically damped.
d) None of the mentioned:
This option can be ruled out based on the analysis above.
Therefore, the correct answer is option 'B': Overdamped response.
To determine the type of response, we need to analyze the denominator of the transfer function.
1. Find the roots of the denominator:
The roots of the denominator can be found by solving the quadratic equation s^2 - 11s + 30 = 0. The roots are s = 6 and s = 5.
2. Classify the response based on the roots:
The type of response is determined by the nature of the roots. In this case, we have two distinct real roots: s = 6 and s = 5.
a) Underdamped response:
An underdamped response occurs when the roots are complex conjugates with a non-zero imaginary part. Since the roots in this case are real, the response cannot be underdamped.
b) Overdamped response:
An overdamped response occurs when the roots are real and distinct. In this case, the roots are distinct (s = 6 and s = 5), indicating an overdamped response.
c) Critically damped response:
A critically damped response occurs when the roots are real and repeated. Since the roots in this case are distinct, the response cannot be critically damped.
d) None of the mentioned:
This option can be ruled out based on the analysis above.
Therefore, the correct answer is option 'B': Overdamped response.
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The current response of a network to a unit step input is Io(s) = 10(s + 2)/s(s2+ 11s + 30). The response isa)Under dampedb)Over dampedc)Critically dampedd)None of the mentionedCorrect answer is option 'B'. Can you explain this answer?
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