Hookes law: Calculate the work done by compressing a spring

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1. Homework Statement
Hookes law: Calculate the work done by compressing a spring by x distance

2. Homework Equations
W = Fd
Ee = 1/2 k x^2
F = kx

3. The Attempt at a Solution

I've found two solutions, but only one is correct. I'm confused why it's the second one.

First formula I derived:
W = Fd
F = kx
d = x

Therefore W = kx^2

However, you can also use the elastic potential energy equation which is a modified version of the equation I made which is

W = 1/2 k x^2 - 0

So, why is it the second equation and not the first one? The way I see it, they sort of both are valid. What is wrong with the first one? Work is force * distance, and that's exactly what I'm doing.

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CAF123

Gold Member
The spring force is a function of x, so W = Fd is not valid. You will have to do an integral.

"Hookes law: Calculate the work done by compressing a spring"

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