1. Not finding help here? Sign up for a free 30min 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!

Classical Mechanics problem

  1. Feb 2, 2008 #1
    1. The problem statement, all variables and given/known data

    Problem: Derive eigenvalue equation of motion of a system undergoing free small oscillation in three dimensional space.

    2. Relevant equations

    3. The attempt at a solution

    I want to know if I have correctly written the values of T and V---

    [tex]\ T=[/tex][tex]\frac{1}{2}[/tex][tex]\ m [/tex] [[tex]\dot{x}^2 +\dot{y}^2+ \dot{z}^2[/tex]]

    And [tex]\ V=[/tex][tex]\frac{1}{2}[/tex][tex]\ k [/tex][[tex]\ x^2+\ y^2+\ z^2 [/tex]]

    I m not sure if I have written the write thing...what should be the sign of k.Should I write -ve?And is it OK to assume that the force constants are equal?What would be if they were not equal?Would they simply add like (1/2)(k1+k2) x^2?

    If I can form T and V,I am confident that I will be able to do the rest of calculations.
    Last edited: Feb 2, 2008
  2. jcsd
  3. Feb 2, 2008 #2
    It appears to me that the potential energy would be

    [tex]\ V= [/tex][tex]\frac{1}{2}[/tex][[tex]\ k_1+k_2 [/tex]][tex]\ x^2 [/tex]+...

    From the elimentary knowledge, we know when a spring of natural length is compressed or elongated, workdone on the particle is -(1/2)kx^2. So,...(1/2)kx^2 amount of energy is stored within the spring as potential energy.So, V would be +ve.


    So, we are to omit the factor of half in V in the first post. Please tell me if I am correct.
    Last edited: Feb 2, 2008
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Classical Mechanics problem