Underdamped Oscillation

When the oscillation amplitude decreases continuously, it is called underdamped oscillation. This type of oscillation occurs when the damping force is less than the critical damping value.

Explanation:

1. Damping in Oscillation:
Damping refers to the process of dissipating the energy of an oscillating system, causing it to gradually decay and come to rest. It is usually introduced to reduce the amplitude of oscillations and control the system's response.

2. Types of Damping:
There are three types of damping in oscillations:
- Overdamping: In overdamped oscillation, the system returns to equilibrium without oscillating, and the amplitude decreases more rapidly than in other types of damping.
- Underdamping: Underdamped oscillation occurs when the system returns to equilibrium but overshoots before settling down, resulting in oscillations with a gradually decreasing amplitude.
- Critically Damped: Critically damped oscillation is a special case where the system returns to equilibrium without overshooting or oscillating. It provides the fastest approach to equilibrium without oscillations.

3. Underdamped Oscillation:
In underdamped oscillation, the damping force is less than the critical damping value. As a result, the system's response includes oscillations with a decreasing amplitude. The time taken for the oscillations to decay and reach zero amplitude is longer than in critically damped oscillation.

4. Characteristics of Underdamped Oscillation:
- Overshoot: Underdamped oscillation exhibits overshoot, where the system's response goes beyond the equilibrium position before settling down.
- Oscillatory Behavior: The system oscillates back and forth around the equilibrium position, with the amplitude gradually decreasing over time.
- Time Period: The time period of underdamped oscillation remains constant, as long as the damping force remains less than the critical damping value.

Conclusion:
When the oscillation amplitude decreases continuously, it is referred to as underdamped oscillation. This type of oscillation is characterized by overshoot and a gradually decreasing amplitude. It occurs when the damping force is less than the critical damping value.