# Modeling movement of a solid in H20

1. Apr 8, 2009

### NBAJam100

1. The problem statement, all variables and given/known data

Im pretty much looking for a little push in the right to direction as to how to get me started on using a differential equation to model the up and down movement of a solid cube in water when a.) it is never submerged, and b.) when it can be completely submerged.

3. The attempt at a solution

I looked at it from a physics point of view first:

I used EF=ma... I started when it is balanced... so Fb=Fw... but im not quite sure where to go from there. I realize that when you apply a force, it will move in a wave motion with damping that will eventually cause it to reach equilibrium again.

Using some differential equations-

mx(double dot)+bx(dot)+kx=Fcos(omega*t).

Where k is the restoring force, b is the resistance to movement, and m is the mass. So, i figure I could use -F/x and plug that in for k, and for b I could find a formula for water induced drag/friction...?

Could anyone give me a little push in the right direction here

2. Apr 8, 2009

anyone?

3. Apr 8, 2009

### Dick

Fluid friction is extremely difficult to model in any detail. Where is this problem coming from? Why do you think it's one you should be able to solve unless you are given a simplified model? I can't.

4. Apr 8, 2009

### NBAJam100

Well, its a chapter exercise in my one book that Ive been studying from: Differential Equations by Blanchard. Maybe they dont want the exact fluid friction numbers but the general solution of just letting it equal a variable (which would seem too simple...).

They didnt tell you anything specific about the solid cube itself, just that it is there, and it oscillates.

But the question is do-able and I doubt its that tough considering it was from my first DE course.