Skip to main content

# 4.6.1.5: Neutral frequency of Floating Bodies

This case is similar to pendulum (or mass attached to spring). The governing equation for the pendulum is $ll\ddot{\beta} - g\beta = 0 \tag{61}$ Where here $$ll$$ is length of the rode (or the line/wire) connecting the mass with the rotation point. Thus, the frequency of pendulum is $$\frac{1}{2\pi}\sqrt{\frac{g}{ll}}$$ which measured in $$Hz$$. The period of the cycle is $$2\pi \sqrt{ll/g}$$. Similar situation exists in the case of floating bodies. The basic differential equation is used to balance and is $I\ddot{\beta} - V \rho_{s} \overline{GM} \beta = 0 \tag{62}$ In the same fashion the frequency of the floating body is $\frac{1}{2\pi}\sqrt{\frac{V\rho_{s}\overline{GM}}{I_{body}}}\tag{63}$ and the period time is $2\pi\sqrt{\frac{I_{body}}{V\rho_{s}\overline{GM}}}\tag{64}$ In general, the larger $$\overline{GM}$$ the more stable the floating body is. Increase in $$\overline{GM}$$ increases the frequency of the floating body. If the floating body is used to transport humans and/or other creatures or sensitive cargo it requires to reduce the $$\overline{GM}$$ so that the traveling will be smoother.

### Contributors

• Dr. Genick Bar-Meir. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or later or Potto license.