Undamped oscillation:
Undamped oscillation refers to a type of oscillation where the amplitude of the oscillations remains constant over time. In other words, the oscillations do not experience any damping or loss of energy. This type of oscillation is idealized and does not occur in real-world systems due to factors such as friction, air resistance, and other forms of energy dissipation.

Explanation:
When an oscillating system is undamped, it means that there are no external forces acting on the system that cause the energy of the oscillations to dissipate over time. In such a system, the total energy remains constant, resulting in oscillations of constant amplitude.

Damped oscillation:
In contrast, damped oscillation occurs when there is an external force or friction acting on the system, causing the energy of the oscillations to gradually decrease over time. As a result, the amplitude of the oscillations decreases as the energy is dissipated.

Balanced oscillation:
The term "balanced oscillation" is not commonly used in the context of describing the behavior of oscillating systems. It is not a correct term to describe the condition of constant amplitude oscillations.

Unbalanced oscillation:
Similarly, the term "unbalanced oscillation" does not accurately describe the behavior of oscillating systems. It may refer to a situation where the forces acting on the system are not in equilibrium, leading to irregular or chaotic oscillatory motion.

Conclusion:
The correct term to describe oscillations of constant amplitude is "undamped oscillation." This refers to an idealized situation where there is no energy loss or damping in the system. Real-world systems often experience damping due to various factors, and therefore, undamped oscillations are not commonly observed.