# Day 90: Linearizing Data with Desmos

*AP Physics C:* Students are determining the relationship between the mass of spring oscillator and the resulting angular frequency. Linearization of data is an expected skill on the AP exam, and this lab is good for that because the data must be linearized twice.

The black data points are the original data (mass, angular frequency). Since it looks like an inverse relationship, we attempt to linearize it by making a new table and graphing (1/mass, angular frequency) — which are the red data points. This clearly isn’t linear, but it looks like a side opening parabola (ie, square root function). So we linearize again by making a third table and graphing (sqrt(1/mass), angular frequency — which are the blue data points. This looks straight! So we add *y* = *mx* to the window and use the slider to find the slope that fits the blue data points (0.49 in this case). Now we use our linearized equation to write an equation to fit the original data (black curve, *y *= (0.49)sqrt(1/*x*)) which works!

Here’s a link to the Desmos file so you can play around with it:

https://www.desmos.com/calculator/ckis9ogpdd

I really like how in the table, Desmos leaves the entries as is, without converting to decimal. For example, leaving it as sqrt(1/0.1) rather than 3.16. This is a nice visual reminder of how we are transforming the data in order to linearize it.