# Thread: Need help finding equation for this graph

1. ## Need help finding equation for this graph

ext press coeff.pdfHi,
I am trying to find the equation used to generate this graph shown in the attachment (any one of the lines).
I suspect it is some type of log function, but I have been away from higher math for many, many years.
Any help would be greatly appreciated.
Thanks,
Flygirl
ext press coeff.pdf

2. ## Re: Need help finding equation for this graph

You can probably use fourier series to represent this graph over the different intervals

3. ## Re: Need help finding equation for this graph

Originally Posted by flygirl71
ext press coeff.pdfHi,
I am trying to find the equation used to generate this graph shown in the attachment (any one of the lines).
I suspect it is some type of log function, but I have been away from higher math for many, many years.
Any help would be greatly appreciated.
Thanks,
Flygirl
ext press coeff.pdf
Hi flygirl71!

That looks to be some sort of Bode plot.

For instance a Bode plot of $\displaystyle \frac{s + 10}{s + 1}$ looks like this (link included).
It is typically approximated by a straight-line-plot as you have, with corner points at s=1 (down) and s=10 (back to horizontal).

4. ## Re: Need help finding equation for this graph

None of the standard functions, except for the absolute value, has a graph consisting of straight line segments. Such graphs can be produced by piecewise-defined function. The linear function that goes through points $\displaystyle (x_1, y_1)$ and $\displaystyle (x_2,y_2)$ is given by $\displaystyle y(x)=y_1+\frac{y_2-y_1}{x_2-x_2}(x-x_1)$. The top graph goes through (10, -3.2) and (500, -2.3). Therefore, the middle portion of the top graph is given by $\displaystyle g(x)=-3.2+\frac{-2.3-(-3.2)}{490}(x-10)$, and the full top graph is given by

$\displaystyle f(x)=\begin{cases}-3.2 & x\le 10\\g(x) & 10<x<500\\ -2.3 & x\ge500\end{cases}$

Another way to define f is using min and max functions.

$\displaystyle f(x)=\max(-3.2,\min(-2.3,g(x)))$