# Homework Help: Coupled oscillator; frequency?

1. Mar 31, 2010

### philnow

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 $$\alpha\frac{d^2x_a}{dt^2}$$ and the coupling force exerted on oscillator B is $$\alpha\frac{d^2x_b}{dt^2}$$ where $$\alpha$$ 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. Mar 31, 2010

### vela

Staff Emeritus
Start by writing the equation of motion for both oscillators.

3. Mar 31, 2010

### mathman44

That's where I'm stuck...

$$m\frac{d^2x_a}{dt^2}=\alpha\frac{d^2x_a}{dt^2}$$
$$m\frac{d^2x_b}{dt^2}=\alpha\frac{d^2x_b}{dt^2}$$

?

4. Mar 31, 2010

### mathman44

I'd be glad to show more work if I knew what to do with this coupling constant!

5. Mar 31, 2010

### vela

Staff Emeritus
Those equations say the only force on the masses is the coupling force. What about the restoring force?

6. Mar 31, 2010

### mathman44

$$m\frac{d^2x_a}{dt^2}=\alpha\frac{d^2x_a}{dt^2} - k(x_a)$$
$$m\frac{d^2x_b}{dt^2}=\alpha\frac{d^2x_b}{dt^2} - k(x_b)$$