If the characteristic equation of a closed-loop system is s2 + 2s + 2 = 0, then the system isSelect one:a. Undampedb. Under dampedc. Critically dampedd. Overdamped
Question
If the characteristic equation of a closed-loop system is s2 + 2s + 2 = 0, then the system isSelect one:a. Undampedb. Under dampedc. Critically dampedd. Overdamped
Solution
To determine the damping characteristics of the closed-loop system, we need to analyze the characteristic equation s^2 + 2s + 2 = 0.
Step 1: Identify the coefficients of the characteristic equation. In this case, the coefficients are: a = 1 b = 2 c = 2
Step 2: Calculate the discriminant (D) using the formula D = b^2 - 4ac. Substituting the values, we get: D = (2)^2 - 4(1)(2) = 4 - 8 = -4
Step 3: Analyze the value of the discriminant:
- If D > 0, the system is overdamped.
- If D = 0, the system is critically damped.
- If D < 0, the system is underdamped or undamped.
In this case, since D = -4, which is less than 0, the system is either underdamped or undamped.
Therefore, the correct answer is: c. Critically damped or d. Overdamped
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