In a stable system, what happens to the transient response?

• A. It grows indefinitely
• B. It remains constant
• C. It decays, and the state returns to the initial equilibrium
• D. It oscillates between positive and negative infinity

Answer: (C)

In a stable system, the transient response typically decays over time, allowing the system to return to its initial equilibrium state. This process occurs because the system is designed to dissipate transient behaviors, such as overshoots or spikes, in response to changes. Stability implies that any deviations from equilibrium will diminish rather than amplify, leading to a gradual stabilization.

In contrast, options that suggest indefinite growth or persistent oscillation describe unstable systems. An indefinite growth would mean that the system cannot return to equilibrium, indicating instability. Similarly, if the transient response oscillates between extremes, this would also imply an inability to reach stability. Therefore, option C is the correct interpretation of behavior in a stable system, where the transient response naturally diminishes, allowing the system to stabilize at a steady state.