So the question goes if I has a spring with spring constant $k$ and two masses attached to this spring (one on either side) what is the resonant frequency of the system in terms of $m$ and $k$?

 

Diagram of system:

 

[m]-////-[m]

Now the real problem I'm having is trying to decide what the forces are acting on the system in order to come up with my differential equation? I know that for a horizontal spring say attached to wall we can take the differential equation

$$m\frac{d^2 x}{d t^2}+kx= 0$$ And then use the equation $Asin(\omega t^2+\phi)$ as a solution and say this is true when $\omega= \sqrt{\frac{k}{m}}$

But I was thinking maybe I could just use the differential equation $$m\frac{d^2 x}{d t^2}+2kx= 0$$ but I feel like that may be too simple? Is there something I'm missing? Any help would be appreciated! :)

Note: None of this system is undergoing any damping

So the question goes if I has a spring with spring constant $k$ and two masses attached to this spring (one on either side) what is the resonant frequency of the system in terms of $m$ and $k$?

Diagram of system:

[m]-////-[m]

Now the real problem I'm having is trying to decide what the forces are acting on the system in order to come up with my differential equation? I know that for a horizontal spring say attached to wall we can take the differential equation

$$m\frac{d^2 x}{d t^2}+kx= 0$$ And then use the equation $Asin(\omega t^2+\phi)$ as a solution and say this is true when $\omega= \sqrt{\frac{k}{m}}$

But I was thinking maybe I could just use the differential equation $$m\frac{d^2 x}{d t^2}+2kx= 0$$ but I feel like that may be too simple? Is there something I'm missing? Any help would be appreciated! :)

Note: None of this system is undergoing any damping

So the question goes if I has a spring with spring constant k and two masses attached to this spring (one on either side) what is the resonant frequency of the system in terms of m and k? (diagram of system)

[m]-////-[m]

Now the real problem I'm having is trying to decide what the forces are acting on the system in order to come up with my differential equation? I know that for a horizontal spring say attached to wall we can take the differential equation

$$m\frac{d^2 x}{d t^2}+kx= 0$$ And then use the equation $Asin(\omega t^2+\phi)$ as a solution and say this is true when $\omega= \sqrt{\frac{k}{m}}$

But I was thinking maybe I could just use the differential equation $$m\frac{d^2 x}{d t^2}+2kx= 0$$ but I feel like that may be too simple? Is there something I'm missing? Any help would be appreciated! :)

Note: None of this system is undergoing any damping

So the question goes if I has a spring with spring constant $k$ and two masses attached to this spring (one on either side) what is the resonant frequency of the system in terms of $m$ and $k$?

Diagram of system:

[m]-////-[m]

Now the real problem I'm having is trying to decide what the forces are acting on the system in order to come up with my differential equation? I know that for a horizontal spring say attached to wall we can take the differential equation

$$m\frac{d^2 x}{d t^2}+kx= 0$$ And then use the equation $Asin(\omega t^2+\phi)$ as a solution and say this is true when $\omega= \sqrt{\frac{k}{m}}$

But I was thinking maybe I could just use the differential equation $$m\frac{d^2 x}{d t^2}+2kx= 0$$ but I feel like that may be too simple? Is there something I'm missing? Any help would be appreciated! :)

Note: None of this system is undergoing any damping