I am making an uncertainty exercise from a simple Physics experiment based on deriving the equivalent spring constant for a series combination of springs. The mathematical model for the combination of spring is derived. The spring constant of the individual springs, as well as that of the combination is measured by suspending weights.
The uncertainty in the equivalent spring constant from the mathematical model is calculated by transferring the uncertainty in the measurement of the individual springs. This, as I understand, constitutes the uncertainty based on the derived mathematical model. The uncertainty in the equivalent spring constant is also calculated from the experiment.
I am trying to understand how to represent these uncertainties on a graph to justify the validity of the derived model. One way, as I figured, is to take the maximum and minimum uncertainties from the mathematical model and plot two lines (since the model is expected to be linear) for the measurement which can serve as the "bounds" of the mathematical model. This would mean that the mathematical model is valid as long as the experimental measurement lies within this bound. Or that is how I understand it. But I am unable to reconcile the uncertainty in the equivalent spring constant which comes from the actual measurement done by suspending weights.