1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    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


    User Avatar
    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
    Last edited: Sep 22, 2010
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: SHM w/ complicated restoring force
  1. SHM question (Replies: 18)

  2. SHM and Gravitation (Replies: 3)

  3. W = Integral force (Replies: 4)