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Coupled oscillator; frequency?

  • Thread starter philnow
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  • #1
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Homework Statement



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.

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?
 

Answers and Replies

  • #2
vela
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Start by writing the equation of motion for both oscillators.
 
  • #3
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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]

?
 
  • #4
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I'd be glad to show more work if I knew what to do with this coupling constant!
 
  • #5
vela
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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]

?
Those equations say the only force on the masses is the coupling force. What about the restoring force?
 
  • #6
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[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]
 

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