Underdamped second-order systems are commonly used to model various physical systems in engineering. These systems exhibit oscillatory behavior in their step response, which can be characterized by several parameters, including the peak overshoot.

The peak overshoot is defined as the maximum percentage overshoot of the response curve with respect to the final steady-state value. It is a measure of how much the response exceeds the desired value before settling down. The peak overshoot occurs when the response reaches its maximum amplitude during the transient period.

The options given in the question are related to different aspects of the step response, and we need to determine which one is explicitly indicative of the peak overshoot.

Let's analyze each option:

a) Settling time: The settling time is the time taken by the response to reach and stay within a certain tolerance band around the final steady-state value. It is not directly related to the peak overshoot and depends on the desired level of accuracy.

b) Rise time: The rise time is the time taken by the response to rise from a specified lower threshold to a specified upper threshold. It is also not directly related to the peak overshoot and depends on the desired time for the response to reach a certain level.

c) Natural frequency: The natural frequency of a system determines the rate at which it oscillates in the absence of damping. While the natural frequency indirectly affects the peak overshoot, it is not explicitly indicative of it.

d) Damping ratio: The damping ratio (ζ) quantifies the level of damping in the system. It is the ratio of the actual damping coefficient to the critical damping coefficient. The damping ratio is directly related to the peak overshoot. Higher damping ratios lead to lower peak overshoots, while lower damping ratios result in higher peak overshoots. Therefore, the damping ratio is explicitly indicative of the peak overshoot.

In summary, the correct answer is option 'D' - damping ratio. The damping ratio of an underdamped second-order system directly determines the peak overshoot in the step response. Higher damping ratios result in lower peak overshoots, while lower damping ratios lead to higher peak overshoots.