Eccentric rotation of a trebuchet arm

[meisadam]

If the word eccentric is not used correctly, please correct me.

Homework Statement

I am constructing a mathematical model of trebuchet throw. For the throwing part, I simply use the relation $$ΔE_p = E_k$$, so the change of potential gravitational energy goes into the rotational kinetic energy. I succesfully built the model, but it is oversimplified in at least one point, the arm does not rotate around a point that is "included" in it, but the pivot point is 8 cm above it. What equations can I use to calculate the changes in potential gravitational energy of such body and its moment of inertia?

Homework Equations

That's my question

The Attempt at a Solution

I have a complete model of the situation assuming the pivot point is included in the arm, but have no clue how to make it eccentric.

 

[Spinnor]

How hard would it be to sketch and scan what you are talking about, or to google image search and find something close to what you have. I'm not clear what you have and a picture is worth a thousand words. Is it built like the following?



or this,

http://www.youtube.com/watch?v=3hCyQIWmzS8&feature=related

 

[meisadam]

Naturally, here it is.
I also don't use the sling to make the model simplier.

http://img851.imageshack.us/img851/6825/apmechimg010.jpg

 

[Spinnor]

Consider the equilibrium configuration of your design when you let it go, it will be significantly less then vertical. The arm will only move about 45 degrees, 90 degrees for the other design. The large mass moves less vertically so your projectile has less energy.