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If the characteristic equation of the closed loop system is s2 + 2s + 2 = 0, then the system is:
- a)Over damped
- b)Critically damped
- c)Undamped
- d)Underdamped
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
If the characteristic equation of the closed loop system is s2 + 2s + ...
The given equation is: s2 + 2s + 2 = 0
It is a second-order differential equation. The Laplace transform of a standard form of a second-order differential equation is:
Comparingthe value we get:
Comparingthe value we get:
Thus, the system is underdamped.
Hence, the correct answer is an option (d).
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If the characteristic equation of the closed loop system is s2 + 2s + ...
Answer:
To determine the behavior of the system, we need to analyze the roots of the characteristic equation. The characteristic equation of the closed-loop system is given as:
s^2 + 2s + 2 = 0
To find the roots, we can use the quadratic formula:
s = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = 2, and c = 2. Substituting these values into the quadratic formula, we get:
s = (-2 ± √(2^2 - 4(1)(2))) / (2(1))
s = (-2 ± √(4 - 8)) / 2
s = (-2 ± √(-4)) / 2
Since the discriminant (√(b^2 - 4ac)) is negative, we have complex roots. Let's simplify the equation further:
s = (-2 ± j√(4)) / 2
s = (-2 ± 2j) / 2
s = -1 ± j
From the roots, we can determine the nature of the system response:
1. Real parts of the roots: The real parts of the roots are both -1, indicating that the system is underdamped. This means that the system response will oscillate and take some time to reach a steady-state.
2. Imaginary parts of the roots: The imaginary parts of the roots are both 1, indicating that the system response will contain oscillatory behavior with a frequency of 1 rad/s.
Based on these observations, we can conclude that the system is underdamped (option D).
To determine the behavior of the system, we need to analyze the roots of the characteristic equation. The characteristic equation of the closed-loop system is given as:
s^2 + 2s + 2 = 0
To find the roots, we can use the quadratic formula:
s = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 1, b = 2, and c = 2. Substituting these values into the quadratic formula, we get:
s = (-2 ± √(2^2 - 4(1)(2))) / (2(1))
s = (-2 ± √(4 - 8)) / 2
s = (-2 ± √(-4)) / 2
Since the discriminant (√(b^2 - 4ac)) is negative, we have complex roots. Let's simplify the equation further:
s = (-2 ± j√(4)) / 2
s = (-2 ± 2j) / 2
s = -1 ± j
From the roots, we can determine the nature of the system response:
1. Real parts of the roots: The real parts of the roots are both -1, indicating that the system is underdamped. This means that the system response will oscillate and take some time to reach a steady-state.
2. Imaginary parts of the roots: The imaginary parts of the roots are both 1, indicating that the system response will contain oscillatory behavior with a frequency of 1 rad/s.
Based on these observations, we can conclude that the system is underdamped (option D).
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If the characteristic equation of the closed loop system is s2 + 2s + 2 = 0, then the system is:a)Over dampedb)Critically dampedc)Undampedd)UnderdampedCorrect answer is option 'D'. Can you explain this answer?
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