# Coupled oscillator

1. Jul 4, 2013

### Pqpolalk357

1. The problem statement, all variables and given/known data

Two identical undamped oscillators, A and B, each of mass m and natural (angular) frequency $\omega_0$, are coupled in such a way that the coupling force exerted on A is $$\alpha m (\frac{d^2 x_A}{dt^2})$$, and the coupling force exerted on B is $$\alpha m (\frac{d^2 x_B}{dt^2})$$, where $$\alpha$$ is a coupling constant of magnitude less than 1. Describe the normal modes of the coupled system and find their frequencies.

I just need someone to explain to me what is the form of the differential equation with respect to each mass. The rest I can continue.

2. Jul 4, 2013

### Simon Bridge

Last edited by a moderator: May 6, 2017
3. Jul 5, 2013

### Pqpolalk357

Could someone explain to me what is exactly is the "coupling force" ?

4. Jul 5, 2013

### Simon Bridge

It is the force that each pendulum exerts on the other.
In a 2-mass, 3-spring system - it comes from the middle spring.