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Coupled Harmonic Oscillator

  1. Jun 11, 2008 #1
    1. The problem statement, all variables and given/known data
    Two masses are connected via a spring. Write the equations of motion, solve them (x(t)), and find the normal mode frequencies.


    2. Relevant equations
    F=ma
    F=-kx


    3. The attempt at a solution
    I set up two equations:
    [tex]F_{1}=ma_{1} , F_{2}=ma_{2}[/tex]
    [tex]-k(x_{2}-x_{1})=m\ddot{x_{1}} , k(x_{2}-x_{1})=m\ddot{x_{2}}[/tex]

    Then I solved the 2nd force equation for [tex]x_{1}[/tex] and plugged it into the first force equation resulting in:
    [tex]-\ddot{x_{2}}=\ddot{x_{1}}[/tex]

    I really don't know what to do now... Any help would be greatly appreciated!
     
  2. jcsd
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