Understanding Simple Harmonic Motion in a Loaded Floating Log

[falcon0311]

A cylindrical wooden log is loaded with lead at one end so it floats vertically in water. The submerged part is 2.56 m (called L). I'm supposed to show the oscillation is simple harmonic.

Can someone point me in the right direction? For some reason I'm thinking gravity and density play a big part of find the this equation. After that, I can find the period.

 

[Tide]

Gravity pulls the log down and buoyancy pushes it up. The buoyant force is equal to the difference between the weight of the submerged portion of the log and water that would occupy the same volume. If you work these out correctly your equation of motion should look like a simple harmonic oscillator.

 

[swatikiss]

how would you model this motion? How do you find w(omega). D

Do you model this as a spring force on the object? I have a similar problem and am stuck. Thanks!

 

[theFuture]

The bouyant force goes like distance submerged. That will push it up, gravity will push it down. Work out the algrebra and get it into a form where you recognize.