I have been working on some data analysis stuff and I have to linearise this equation so I can plot it as a straight line with form y=mx+c
$$T=2\pi\sqrt{\frac{(k^2 + h^2)}{gh}}$$
Where, T will be the y and h the x, k is a constant but g is a variable.
But no matter how I've manipulated it I can't get just one h. any help or pointers would be appreciated.
I don't believe this can be done with the information you gave us. These are two options:
The most obvious thing you can do is call $x = \sqrt{(k^2+h^2)/gh}$ so that you have a model of the form $T = x/2\pi$, but I'm not sure this is what you're looking for
If you plot this in log scale you'll see that if you around the model behave fairly linear for $h / k \ll 1$ and $h /k \gg 1$. You can Taylor expand the model in these two regimes up to linear order in log scale