Finding equivalent spring constant for a rigid bar on two springs

[enceladu5]

Homework Statement

I have a attached a photo of the problem I'm trying to solve.

I defined x1 as displacement of the bar at the k1 spring, and did so similarly for x2 & k2.

It is known k1=k2 as the bar lies flat in equilibrium before the force is applied.+

By taking the moment about F, I found x2=x1*L1/L2

So far i have F=Ke*X=k1*x1+k2*x1*(L1/L2)
where Ke is the equivalent spring constant.
I'm stuck finding a relation between X and x1.

I'd like to thank any who can help in advance

 

[Chestermiller]

k1 is not necessarily equal to k2 before the force is applied (unless the bar has weight, which, in this problem it doesn't). Your displacement X at the load application location is related to x1 and x2 by a simple geometry problem.