Work done by springs in a series

[sillybean]

Homework Statement

Two springs, with force constants k1 and k2, are connected in series, as shown in the figure

How much work is required to stretch this system a distance x from the equilibrium position?

Homework Equations

W=1/2kx^2

The Attempt at a Solution

I have no idea how to derive this. I mean I've looked on the wikipedia article on hooke's law and figured that I just change the equation to W=1/2 (1/k1 + 1/k2)x^2

I'm guessing the problem with this is that the distances that the two stretch are not equal because of the different spring constants but I don't know how to go about showing this in an equation.

 

[||spoon||]

is that 1/(2kx^2) or (1/2k)x^2

 

[sillybean]

it is (1/2k)x^2

 

[||spoon||]

using 1/kt=1/k1+1/k2. Substitute into elastic potential energy equation.

Edit: forget that... Misunderstood your question I think.

 

[sillybean]

i did that
W=1/2 (1/k1 + 1/k2)x^2

and this was wrong

 

[||spoon||]

i did that
W=1/2 (1/k1 + 1/k2)x^2

and this was wrong

I know. That'd why I edited and said forget it, Lol.

 

[sillybean]

ah i see. so any other takers.

 

[sillybean]

still need help. is my theory about distances being different right?