Two bars connected by a spring on a floor with friction

[Null_Void]

No.

$Fx - 1/2kx^2 - μm_2gx= 0$
Is this the right equation?

 

[PeroK]

$Fx - 1/2kx^2 - μm_2gx= 0$
Is this the right equation?

It is. It's useful because that's the point at which $m_2$ stops. And that's the point at which the force in the spring is at its maximum.

 

[Null_Void]

It is. It's useful because that's the point at which $m_2$ stops. And that's the point at which the force in the spring is at its maximum.

Ah I get it now. Combining this with the equation @haruspex pointed out, I'll get
$F = μ(m_1g/2 + m_2g)$ which is the correct answer, Thanks for your help everyone!