Equivalent spring constant of a system

[theBEAST]

Homework Statement

and the attempt at a solution[/B]
I tried to find the equivalent sprint constant using two points of equivalence. The first is with respect to theta. The second is with respect to the datum x as shown in the images below. The two methods yield two different answers which is not what I expected. Did I do something wrong?

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?