Looking for a function in system of DE

[sludger13]

I'm looking for prescription of function $f$ with behavior:

putted in this system of DE solving some simple functions $r_{1}(x)$ and $r_{2}(x)$:
$\frac{d^{2}r_{2}(x)}{dx^{2}}=\frac{f(r_{2}(x)-r_{1}(x))}{C}$
$\frac{d^{2}r_{1}(x)}{dx^{2}}=-\frac{f(r_{2}(x)-r_{1}(x))}{K}$

$r_{2}(x)-r_{1}(x)>0;f(r_{2}(x)-r_{1}(x))>0;C,K>0$

 

[maajdl]

Why not a straight line?

 

[maajdl]

3.31143 - 1.37286 x + 0.135714 x^2

fits more or less the lower curve