If the characteristic equation of a closed-loop system is s2 + 2s + 2 = 0, then the system isSelect one:a. Undampedb. Critically dampedc. Overdampedd. Under damped
Question
If the characteristic equation of a closed-loop system is s2 + 2s + 2 = 0, then the system isSelect one:a. Undampedb. Critically dampedc. Overdampedd. Under damped
Solution
To determine the type of damping of the system, we need to analyze the characteristic equation s^2 + 2s + 2 = 0.
Step 1: Calculate the discriminant (D) of the characteristic equation. The discriminant is given by D = b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation.
In this case, a = 1, b = 2, and c = 2. So, D = (2)^2 - 4(1)(2) = 4 - 8 = -4.
Step 2: Analyze the value of the discriminant. If the discriminant is positive (D > 0), the system is underdamped. If the discriminant is zero (D = 0), the system is critically damped. If the discriminant is negative (D < 0), the system is overdamped.
In this case, the discriminant is negative (D = -4), so the system is overdamped.
Therefore, the correct answer is: c. Overdamped.
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