The physics behind a spring

Hello

The formula for calculating the force a spring pulls with looks like this:

F = k * x

Where :
F = Force (N)
x = the extension of the spring
k = the spring constant (my guess that€™s the English word for it, its directly translated)

I asked in the Swedish part of this forum for the formula for calculating the energy contained in the same spring. The answer was:

E = (k * x^2)/2

Where:
E = energy (Joule)
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

All fine I thought, but... carefully testing showed that, no matter how odd it seems, the formula for the force (in the case of this spring) should be written like this:

F = k * x + m

Where:
F 1
m = a constant (in this case approximately 0,81)

If you don€™t believe me look at this table:
http://user.tninet.se/~qny348e/diablo2/fj%e4derkonstanten.jpghttp://user.tninet.se/~qny348e/diabl...konstanten.jpg

And this graph:
http://user.tninet.se/~qny348e/diablo2/graf.jpghttp://user.tninet.se/~qny348e/diablo2/graf.jpg

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

So the question is, what€™s the formula for calculate the energy contained within this mysterious spring?

Best regards
Petter Nilsson

the energy in a spring is just the integral of the force with respect to extention, in this case that is the integral of k * x + m

= (k * x^2)/2 + (m * x)

Joe Townsend

also beware that not all of the energy you try to put into the spring goes there, if you took force - extention readings when unloading the sping instead of loading it then you would get a different line. The area under the unloading line would be smaller and the difference between that area and the loading line area is the energy lost due to hysterisis.

Joe Townsend

I was, at first, puzzled by your findings. However, I remembered that helical steel springs can have a degree of internal tension when unextended, so that a minimum force is needed to get any extension. This would correspond to m in your test results.

I came into this thread, and my first thought was *Man I need to get my eyes tested*, as I was originally here to say this thread was in the wrong place as I read The psychics behind a spting

My second thought was *Huh*

Im not meaning to dumb this thread down, but could we please have physics for idiots!

Thank you for your help.

Matty go back to your cave if you cant stand science. I for one am an absolute dummy in this field but applaud and encourage more of this on the forum because it is darn well useful ! If you cant understand it, ask someone who might(Private Messaging is so wonderful).
Well done Peter !