What equation produces this curve? I'm working on an engineering project, and I'd like to be able to input an equation into my CAD software, rather than drawing a spline.
The spline is pretty simple - a gentle curve which begins and ends horizontal.
Is there a simple equation for this curve?
Or perhaps two equations, one for each half?
I can also work with parametric equations, if necessary.


Assuming you mean
$$\begin{align}
y(0) &= 40 \\
y(120) &= 0 \\
\dot{y}(0) &= 0 \\
\dot{y}(120) &= 0
\end{align}$$
then a simple cubic will do:
$$y(x) = \frac{x^3}{21600} - \frac{x^2}{120} + 40$$
At range $x=0\dots120$, it looks like this:


You can find these very easily. In general, a cubic curve is
$$y(x) = C_3 x^3 + C_2 x^2 + C_1 x + C_0$$
and its derivative
$$\dot{y} = \frac{d y(x)}{d x} = 3 C_3 x^2 + 2 C_2 x + C_1$$
Fix four values, each fixing one of the constants, and that's it.
