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!

Normal modes, 2 masses, 2 springs

  1. Jul 20, 2007 #1
    1. The problem statement, all variables and given/known data
    hey, this is my first time using this forum and was wondering if i could have some help with this normal modes question.

    suspended from a ceiling is in order: a spring of spring constant ([tex]k_{2}[/tex]), a mass (m), a spring with spring constant ([tex]k_{1}[/tex]), and another mass (m)

    calulate the normal mode frequencies [tex]\alpha_{1}[/tex], [tex]\alpha_{1}[/tex] sorry can't find the omega symbol.

    attempted solution:
    let the displacement of the higher mass be x and the displacement of the lower mass be y.

    m[tex]\ddot{x}[/tex]=-[tex]k_{2}[/tex]x + [tex]k_{1}[/tex](y-x)

    [tex]\left| \alpha^{2} - (\frac{k_{2}}{m} + \frac{k_{1}}{m}) -----\frac{k_{1}}{m} \right|[/tex]
    [tex]\left| \frac{k_{1}}{m} -------- \alpha^{2} - \frac{k_{1}}{m} \right|[/tex] = 0

    determinant = 0

    so [tex]\alpha^{2}[/tex] = 1/2[ ([tex]\frac{k_{2}}{m}[/tex]+ [tex]\frac{2k_{1}}{m}[/tex]) +- sqrt[([tex]\frac{k_{2}}{m}[/tex]+ [tex]\frac{2k_{1}}{m}[/tex])^2 – 4([tex]\frac{k_{2}*k_{1}}{m^2}[/tex])]]

    after simplifying it doesn't work when I use to try and solve for the amplitude ratios.
    please advise, thanks.
    p.s. is there a simpler equation writer i could download and use here or should i just persevere and try to use this embedded one?
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Discussions: Normal modes, 2 masses, 2 springs
  1. 2 masses 3 springs (Replies: 12)