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The voltage response of a network to a unit step input is Vo(s) = 10/s(s2 + 8s + 16). The response is
- a)under damped
- b)over damped
- c)critically damped
- d)can’t be determined
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The voltage response of a network to a unit step input is Vo(s) = 10/s...
The characteristic equation has real and repeated roots (-4, -4). Hence it is critically damped.
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The voltage response of a network to a unit step input is Vo(s) = 10/s...
Analysis of the Voltage Response:
Understanding the nature of the voltage response of a network to a unit step input involves analyzing the given transfer function Vo(s) = 10/s(s^2 + 8s + 16). In this case, the system is represented by a second-order differential equation.
Characteristics of the Response:
To determine the damping of the response, we need to examine the roots of the denominator polynomial of the transfer function. The roots of the characteristic equation s^2 + 8s + 16 = 0 can be calculated using the quadratic formula.
Calculation of Roots:
The roots of the characteristic equation are s = -4 and -4. Since the roots are real and equal, the system is critically damped.
Interpretation of Critically Damped System:
A critically damped system responds quickly to changes in the input without any oscillations or overshoot. It achieves the fastest response without introducing any oscillations.
Conclusion:
Based on the analysis of the transfer function and the roots of the characteristic equation, the voltage response of the network to a unit step input is critically damped. This indicates that the system responds efficiently and quickly to changes in the input signal without exhibiting any oscillations or overshoot.
Understanding the nature of the voltage response of a network to a unit step input involves analyzing the given transfer function Vo(s) = 10/s(s^2 + 8s + 16). In this case, the system is represented by a second-order differential equation.
Characteristics of the Response:
To determine the damping of the response, we need to examine the roots of the denominator polynomial of the transfer function. The roots of the characteristic equation s^2 + 8s + 16 = 0 can be calculated using the quadratic formula.
Calculation of Roots:
The roots of the characteristic equation are s = -4 and -4. Since the roots are real and equal, the system is critically damped.
Interpretation of Critically Damped System:
A critically damped system responds quickly to changes in the input without any oscillations or overshoot. It achieves the fastest response without introducing any oscillations.
Conclusion:
Based on the analysis of the transfer function and the roots of the characteristic equation, the voltage response of the network to a unit step input is critically damped. This indicates that the system responds efficiently and quickly to changes in the input signal without exhibiting any oscillations or overshoot.
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The voltage response of a network to a unit step input is Vo(s) = 10/s(s2+ 8s + 16). The response isa)under dampedb)over dampedc)critically dampedd)can’t be determinedCorrect answer is option 'C'. Can you explain this answer?
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