An underdamped system is a type of oscillating system that experiences oscillations that gradually decrease in amplitude over time. This occurs when the damping force is not strong enough to prevent oscillations entirely, allowing the system to oscillate back and forth around an equilibrium position. Common examples include a swinging pendulum or a mass on a spring that is lightly damped. In an undamped system, the oscillations continue indefinitely, while in an underdamped system, the oscillations will eventually fade away. The behavior of such systems is often described using concepts from control theory and mechanical engineering, where understanding the damping ratio is crucial for predicting system performance.