The time oscillation of a floating body refers to the period of its natural oscillations when subjected to external disturbances such as waves or wind. The metacentric height is a parameter that determines the stability of a floating body and is defined as the distance between the center of gravity (G) and the metacenter (M). The metacenter is the intersection point of the line of action of the buoyant force with the body in its initial upright position.

When the metacentric height increases, the time oscillation of the floating body will be lower. This can be explained by the following factors:

1. Stability: The metacentric height is directly related to the stability of a floating body. A higher metacentric height indicates a greater stability, while a lower metacentric height indicates a lower stability. When the metacentric height is increased, the stability of the floating body is improved, resulting in a lower time oscillation.

2. Restoring Moment: The metacentric height affects the restoring moment acting on the floating body. The restoring moment is the moment created by the buoyant force that acts to restore the body to its original upright position when it is tilted by external forces. A higher metacentric height increases the restoring moment, thereby reducing the time oscillation.

3. Roll Period: The time oscillation of a floating body is also influenced by its roll period, which is the time taken for the body to complete one full oscillation. When the metacentric height is increased, the roll period decreases, resulting in a lower time oscillation.

4. Damping: The metacentric height also affects the damping characteristics of the floating body. Damping refers to the dissipation of energy during the oscillation process. A higher metacentric height leads to increased damping, which helps to reduce the time oscillation.

In conclusion, the time oscillation of a floating body decreases when the metacentric height increases. This is due to the improved stability, increased restoring moment, reduced roll period, and enhanced damping characteristics associated with a higher metacentric height.

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