# Force Integration, UFM

1. Sep 29, 2011

### Caveman11

Hi all,

I am having a problem which is something that I can't think what the reason is. I may well be making a very elementary mistake.

Here it is:

In UFM in order to write the force on the cantilever as a function of the tip surface separation then we must take into account the sample oscillations.

The sample oscillations are given by: $$Acos(\omega t)$$ where A is the oscillation amplitude.

By subtracting this from the tip sample z displacement we obtain the time dependant separation.

z -Acos(\omega t)

Then integrating over one whole oscillation period we obtain

F=\int_{0}^{T}F(z -Acos(\omega t)) dt

However this is where my problem is. In all literature I have read there is a factor of $$\frac{1}{2\pi}$$ infront of the integral.

But I can't think where is has come from?

Any response you have is greatly appreciated.

Thanks