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Simple Harmonic Motion - Acceleration

  1. Jun 28, 2011 #1
    Hi, :smile:

    Assuming that the motion of the hydrogen atom is simple harmonic, its frequency of oscillation, f, is given by the expression:

    f = 1 / 2π * √(k/m)​

    where k is the force per unit displacement between a hydrogen atom and the carbon atom and the m is the mass of a proton.

    (i) Show that the value of k is approximately 560 N/m
    (From previous parts of this question I knew: f = 9.1 x 1013 Hz and the mass was 1.7 x 10-27

    I managed to do this question by rearranging and plugging the numbers in the formula

    However, I am having problems with part (ii)

    (ii) Estimate, using your answers to (c)(i), the maximum acceleration of the hydrogen atom.

    I am thinking either F = ma, where F = kx. In this case, the k I got from the previous question would be the constant k, or the F itself?

    Or use a = -ω2x, using the maximum displacement (I have it from previous part of the question)

    How should I approach the second part with the F = ma format? Is it possible to tackle the problem in those two ways?

    Thanks,
    Peter G.
     
  2. jcsd
  3. Jun 28, 2011 #2

    Doc Al

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    Staff: Mentor

    That method would work, but I don't understand the question. (Of course the k will be the constant k.)

    That works.

    What's the maximum force?
     
  4. Jun 28, 2011 #3
    The maximum force would be the constant multiplied by the maximum displacement?
     
  5. Jun 28, 2011 #4

    Doc Al

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    Staff: Mentor

    Exactly. Now you can use Newton's 2nd law to calculate the maximum acceleration.

    (Be sure to solve it both ways--convince yourself that the methods are equivalent.)
     
  6. Jun 28, 2011 #5
    Ok, will do!

    Thanks!
     
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