Equivalent Spring Constant (3 springs attached to a swinging rod)

[qwerty007]

Homework Statement

Q) Derive the expression for the equivalent spring constant that relates the applied force F to the
resulting displacement x of the system shown in Fig. 1.86. Assume the displacement of the
link to be small.

Homework Equations

I have solved the question but when i checked it on the solution manual, the answer was different. In the solution manual they have approximated the extensions of all the springs as the same but i think they will be different.
Please let me know whether my method is correct or the one in the solution manual.

MY WORKING:
http://www.mediafire.com/view/2bdhs46w9igg83d/IMG_20140510_214819.jpg

solution manual:
http://www.mediafire.com/view/ks0t5btpg5y7d13/IMG_20140510_214607.jpg

The Attempt at a Solution

There are 2 methods and each leading to different values of Keq. Which method should i follow?

 

[paisiello2]

Figure 1.86 wasn't posted but based on the information you provided, I think I like your solution better.

 

[qwerty007]

Thanks for your reply.
Figure 1.86 is the same as what is drawn in my working.

 

[AlephZero]

The only thing that is not absolutely clear from your two attachments is whether the different stiffness of k1, k2, k3 are meant to be the "real" stiffness, or the effective stiffness including effect of the different displacements as the arm rotates.

Assuming they are the real stiffness of the 3 springs, I think your answer is correct.