- #1
skrat
- 748
- 8
Homework Statement
This is not really a homework problem, it's a problem that I am working on and am not able to come to an end of it.
The story is:
I have a certain amount of force, let's call it ##F_0##, that I can distribute on a certain length ##L## just the way I want it to. Meaning that the ##F(x)## can describe any function you can imagine for ##0\%<x<100\%##.
For example, we can set ##F(x)## to be a sum of two Heaviside functions $$F(x)=aH(x)+(b-a)H(x-50)$$ or we can say it is linear or we can say the distribution is Chi squared for ##k=4##, see graphics on the link (https://upload.wikimedia.org/wikipe...i-square_pdf.svg/600px-Chi-square_pdf.svg.png).
Homework Equations
The Attempt at a Solution
My problem here is that I am missing a condition to satisfy. So I have ##F_0## available and any distribution I can think of.
But whichever distribution I choose, I have to normalize it to that ##F_0##. And this is where I am weak. I don't know how to do it, I don't understand the physics behind it.
Because:
Let's assume it is a linear distribution for a moment, so ##F(x)=kx##. But I have no idea how to normalize it to ##F_0##. If I was to integrate it $$\int F(x)dx$$ than I am afraid that would be pressure and not force, but if I was to somehow sum the values ##F(x)## for discrete (with very small steps) ##x## than I am afraid this is wrong, because it massively depends on how small the steps are...
So. Yeah. I'm stuck here. I hope you understood my confused description of the problem, though. :)
ps: I am working in Mathematica, so if there is anything I can do there, just let me know and I can try.
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