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SHM w/ complicated restoring force

  1. Sep 21, 2010 #1
    The problem statement, all variables and given/known data
    An atom of mass m is bonded to surface immobile body by electromagnetic forces. The force binding the atom to the surface has the expression:

    [tex] F= exp\ (a\cos z + b\sin z) + d\tan(z) [/tex]

    where a,b, and d are constants and z is upwards. The equilibrium point is defined to be z=0. The system is subject to Earth's gravity

    For small oscillations, give an approximate expression for the binding force on the atom.

    The attempt at a solution
    Ok so in class we were taught to do the Taylor Series expansion on F(x) and keep the linear term so you can get something that looks like F=-kx . So I got this after doing Taylor Series expansion:

    where [tex] F' = (-a\sin z + b\cos z) exp\ (a\cos z + b\sin z) + d\sec^2 (z) [/tex] then evaluate at z=0 then final result is :

    [tex] F(z)= (b exp(a) + d )z [/tex]

    Since [tex] F(0) [/tex] is always 0 at the equilibrium I took that out of Taylor series and ignored higher order terms.

    Now I'm not sure if I'm going about this the right way? Can someone please tell me if I did this right or not? Much appreciated I love this forum!
     
    Last edited: Sep 21, 2010
  2. jcsd
  3. Sep 21, 2010 #2

    diazona

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    Homework Helper

    You've got the right idea, but you seem to have computed F' incorrectly. Take another look at that calculation.
     
  4. Sep 21, 2010 #3
    How is F' wrong?? :S please explain I just used the chain rule
     
  5. Sep 21, 2010 #4

    diazona

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    Homework Helper

    It's wrong for the F that was in your post when I wrote mine. But after your edit, everything looks OK.
     
  6. Sep 21, 2010 #5
    Thanks
     
    Last edited: Sep 22, 2010
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