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matlabplotdatasetcurve-fittingloglog

Utility of loglog plots in curve fitting inverse square relationship

I have a a bunch of data that I'd like to use to find an unknown parameter in a physical equation.

I'm trying to find a parameter k to characterise the output of a hall effect sensor as a function on input voltage and distance between the sensor and the magnet. However, I've found this function to be inversely proportional to the square of the distance.

I asked my professor about how to use MATLAB to find the unknown parameter, and he told me I could try to fit it by taking the logarithm of both sides of the equation and plotting that, seen as that would make the relationship linear and thus easier to plot.

I'd have to do this in MATLAB and I'm assuming the values I measured would have to be converted by hand before being able to perform any sort of curve fitting on them.

I was wondering if doing that was worth it, and if there is a faster way of doing this.

Thanks :)

Solution

  • In order to easily identify the relationship, for a set input voltage, I had to take the logarithm of the measured distance and the logarithm of the respective output voltages and plot those. Fitting a line through those points then enabled me to see that the coefficient was close enough to -2, confirming the inverse square relationship.

    I then did the same for different input voltages and added everything together on the same plot.