mass between two compression springs

[pierresabiy]

I want to simulate such a system in Simulink.

This is a mass between two compression springs. The springs are compressed to its length eg. the value of 10 mm. Thus then the body force acting k[sub]L[/sub].x[sub]L[/sub] (k[sub]R[/sub].x[sub]R[/sub]). For such a system force is applied the shock 50G for 10ms. The body can be moved so that one spring force no longer act on the mass. (spring is already not mass even touch). Suppose that such a situation can occur in both directions.
Assume for simplicity that the stiffness of the springs EQUATORIAL.
So far I have come to such an equation. I do not agree, however, that e.g. in the fourth image value xr + y negative values​​.
How to edit the equation that it could simulate in Simulink?
I'm thinking not correct?
I would be thankful for any advice.

http://youtu.be/wcAMWxK2iT4

 

[Junimech]

Are you familiar with block diagrams? you should have a block with the inertia 1/m. The output of that block is acceleration. Integrate that signal and you obtain velocity. Integrate again to obtain position x (being it zero at resting position for instance)
The input of the inertia block should be the sum of two (or three components to model F).
FL should be defined as kL*(-x-xL)*(x<0) and FR kR*(x+xR)*(x>0). So the FL and FR signal in Simulink should be generated with feedback of the x position. There are integration blocks in Simulink, as well as sign detection blocks.
In the last integration block, you can define the initial x position.
Finally, the impulse force F can be added with source blocks of Simulink.