Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

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: \begin{equation}Acos(\omega t)\end{equation} where A is the oscillation amplitude.

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

\begin{equation}

z -Acos(\omega t)

\end{equation}

Then integrating over one whole oscillation period we obtain

\begin{equation}

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

\end{equation}

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

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

Any response you have is greatly appreciated.

Thanks

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# Force Integration, UFM

Can you offer guidance or do you also need help?

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