How Do You Calculate the Effective Spring Constant k_eff for Springs in Series?

[ksmith159]

See attached file:
I would like to show theoretically that the first double spring system is equivalent to the second system with only one spring keff. Then I want to derive an expression for keff in terms of k1 and k2.

I think this system is in series and therefore keff =1/k1 +1/k2
but that is probably not even close to the right track...

 

[rock.freak667]

Well for the new spring system

$$F=k_{eff}(x_1+x_2)$$

knowing that F is the same for both springs, can you make an attempt now?

(sorry if I sound harsh,am a bit handicapped at the moment and typing is tedious)