# Visualizing Uncertainties

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.

• Can you clarify what you've actually measured? Have you put $n=1,2,3,...$ identical springs in series and then measured the total spring constant or have you paired up a variety of 'known' springs and measured their effective spring constants? – jacob1729 Sep 1 at 15:37
• Hi. Thanks for your reply. The setup has two springs of different, unknown spring constants. A theoretical model is first derived for the effective spring constant (equivalent spring constant) of the series combination of the two springs. The spring constant of the individual springs is measured together with the uncertainty in the measurements. These uncertainties are then transferred to the equivalent spring constant as per the model. Hope this helps. – Shaz Sep 1 at 18:19