1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Normal Modes of a Triangle Shaped Molecule

  1. Nov 8, 2013 #1
    1. The problem statement, all variables and given/known data
    A molecule consists of three identical atoms located at the vertices of a 45 degree right triangle.
    Each pair of atoms interacts by an effective spring potential, with all spring constants equal
    to k. Consider only planar motion of this molecule. What are 6 normal modes and what do they represent?

    The real stickler of this problem is the set up.

    2. Relevant equations

    See section 10.9.1 in this:

    3. The attempt at a solution
    Basically I started off and did the same thing until they took some approximations starting with 10.109.

    I don't understand how they got 10.110 in the linked file. I think I understand how they got 10.109 and 10.111, since y2,y1 and x3,x1 are zero if you set your coordinates correctly and don't allow the molecule to spin too much.

    The rest of problem is a doable and understandable, I'm just getting stuck on this one part.

    Thank you!
  2. jcsd
  3. Nov 9, 2013 #2


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    Hello, NewNuNeutrino.

    Which line of equation 10.110 are you asking about?
  4. Nov 9, 2013 #3
    I know where he gets d[itex]_{12}[/itex]=[itex]\sqrt{(-a+x_{3}-x_{2})^{2}+(a+y_{3}-y_{2})^{2}}[/itex]
    but I don't know what approximation he uses to get to

    It seems like it should be simple, but I can't figure it out.

    Thank you!
  5. Nov 9, 2013 #4


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    Try to get the expression into a form that you can use ##\sqrt{1+\epsilon} \approx 1+\epsilon/2##

    You might let ##Δx = x_2-x_3## and ##Δy = y_3-y_2## (note the order of subscripts). Then you can write the initial expression as $$d_{23}=\sqrt{(a+Δx)^2+(a+Δy)^2}$$
    Also note that to first order accuracy, ##(a+Δx)^2 \approx a^2+2aΔx##, etc.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted