Final answer:
In a second-order system exposed to a step input, oscillations in the response will occur when the system has two complex conjugate poles, indicating an underdamped condition. No oscillations are expected for overdamped (two real and distinct poles) or critically damped (two real and identical poles) systems.
Step-by-step explanation:
For a second-order system subjected to a step input, the type of response—whether there will be oscillations or not—depends on the nature of the system's poles. Here are the system situations and their expected responses:
- Two complex conjugate poles: The system is underdamped and will experience oscillations about the equilibrium point as it moves towards equilibrium.
- Two real and distinct poles: The system is overdamped and moves slowly towards equilibrium without oscillations.
- Two real and identical poles: The system is critically damped, which indicates it will move to equilibrium as quickly as possible without oscillating.
- One real pole and one complex conjugate pole: This is not a standard second-order system configuration, and the response could be complex but typically would not feature the clear oscillatory behavior of a typical underdamped system with two complex conjugate poles.
The situations that will experience oscillations in their response are systems with two complex conjugate poles, indicative of an underdamped system.