Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Coupled oscillator; frequency?

  1. Mar 31, 2010 #1
    1. The problem statement, all variables and given/known data

    Two identical undamped oscillators are coupled in such a way that the coupling force exerted on oscillator A is [tex]\alpha\frac{d^2x_a}{dt^2}[/tex] and the coupling force exerted on oscillator B is [tex]\alpha\frac{d^2x_b}{dt^2}[/tex] where [tex]\alpha[/tex] is a coupling constant with magnitude less than 1. Describe the normal modes of the coupled system and find their frequencies.

    3. The attempt at a solution

    I know this isn't much of an attempt, but I've searched online and in the text... what am I supposed to do with this coupling constant?
     
  2. jcsd
  3. Mar 31, 2010 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Start by writing the equation of motion for both oscillators.
     
  4. Mar 31, 2010 #3
    That's where I'm stuck...

    [tex]m\frac{d^2x_a}{dt^2}=\alpha\frac{d^2x_a}{dt^2}[/tex]
    [tex]m\frac{d^2x_b}{dt^2}=\alpha\frac{d^2x_b}{dt^2}[/tex]

    ?
     
  5. Mar 31, 2010 #4
    I'd be glad to show more work if I knew what to do with this coupling constant!
     
  6. Mar 31, 2010 #5

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Those equations say the only force on the masses is the coupling force. What about the restoring force?
     
  7. Mar 31, 2010 #6
    [tex]m\frac{d^2x_a}{dt^2}=\alpha\frac{d^2x_a}{dt^2} - k(x_a)[/tex]
    [tex]m\frac{d^2x_b}{dt^2}=\alpha\frac{d^2x_b}{dt^2} - k(x_b)[/tex]
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook