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Force Integration, UFM

  1. Sep 29, 2011 #1
    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: \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
     
  2. jcsd
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