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.

  • $\begingroup$ How does $g$ change with the other variables in the problem? $\endgroup$ – caverac Nov 21 '18 at 13:23
  • $\begingroup$ you may consider a three dimension coordinate and assume z as g. $\endgroup$ – sirous Nov 21 '18 at 14:07
  • $\begingroup$ @caverac I'm not sure however, I think (based on hints further on) that it is somehow incorporated into the gradient of the line. Later it suggests you can calculate and find the error for g from the gradient of the line of least squares which I plot based on the linearised data points. However I obviously can't get the linearised data points without the equation being linearised first. $\endgroup$ – Ethilios Nov 21 '18 at 14:45

I don't believe this can be done with the information you gave us. These are two options:

  1. 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

  2. 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

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