Connected bodies - Spring and 2 blocks

[zorro]

Homework Statement

A block of mass m is connected to another block of mass M by a massless spring of spring constant k. The blocks are kept on a smooth horizontal plane. Initially, the blocks are at rest and the spring is unstretched when a constant force F starts acting on the block of mass M to pull it. Find the max. extension of the spring.

The Attempt at a Solution

I can find the answer working from the reference frame of COM of the system of 2 blocks and spring.

I am interested in finding it from ground frame.

Net force on M, F1 = F-kx, where x is the extension in the spring
Net force on m, F2 = kx

Let the displacements of the two blocks be x1 and x2.

F1x1 + F2x2 =0.5k(x2-x1)² (x2-x1 is the extension produced)

I am unable to find another equation.

 

[cupid.callin]

F1x1 + F2x2 =0.5k(x2-x1)² (x2-x1 is the extension produced)

You should not include F2x2. Only include external forces!
But anyway this even won't give you result

I don't know if you can just subtract the forces or not.
I mean as soon as force F will act, body will start to move ... with even little expansion in spring, m2 will move with force kx'
this force will inc. with time till kx_max
I am not sure if you can just use the initial and final conditions and ignore the intermediate stages!
well I'm still trying and tell you my progress!

 

[zorro]

Did you come up with something?