The unit step response of the transfer function
\( G(s) = \frac{1}{s^2 + 2s + 3} \)
has:
Show Hint
- a damped oscillatory characteristic
- is overdamped
- has a non-zero slope at the origin
- is unstable
The Correct Option is A
Solution and Explanation
Step 1: Analyzing the transfer function.
The transfer function \( G(s) = \frac{1}{s^2 + 2s + 3} \) represents a second-order system. The step response of such a system depends on the nature of its poles.
Step 2: Explanation of options.
- (A) The characteristic equation indicates underdamped behavior, leading to a damped oscillatory response.
- (B) Overdamped systems do not exhibit oscillatory behavior.
- (C) The response does not have a non-zero slope at the origin.
- (D) The system is stable because its poles have negative real parts.
Final Answer: \[ \boxed{\text{A) a damped oscillatory characteristic}} \]
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