Standard Error and Uncertainty Analysis

Hello,

I have a bunch of experimental data and I'm trying to do analyse the data, however this is my first time actually doing anything like this so I have a few questions.

My first experiment is simply a matter or measuring the displacement of a mass attached to a spring when a known force is applied.

The force is applied by a known mass acted upon by gravity.

The masses are 10g, 35g, 51g, I assumed as they were labelled only in grams the uncertainty was +/- 0.5g.

The force then is 9.81*m, the uncertainty is similarly 9.81*u.

Initially I took 5 zero readings for the apparatus, using the mean as the zero reading, and calculated the standard error.

For each amount of force I then took 5 readings of the displacement, and using this calculated the mean and the standard error for each.

I then plotted the mean values of displacement against the force applied. I also plotted maximum values of force vs minimum values of displacement and minimum values of force against maximum values of displacement. Then found the gradients of the three lines to give myself the average and limits of the springs stiffness (k).

So I now have k = 48.0 +/-0.9 N/m

Now I use this value to find the mass principle mass attached to the spring, by setting the mass into free oscillation, measuring the period of the oscillation and then using T=2*Pi*(m/k)^0.5, rearranging for m=(T^2*k)/(4*Pi^2)

For the period I measured 6 periods, of oscillation and did this 3 times, so I calculated the mean period and the standard error from this.

So now I have the period with standard error and the spring stiffness with a limit(?). How do I combine these to get a meaning full error in my final value.

The information I have says to only combine limits or standard errors.

So my question is do I treat stuff as limits and use the rules for adding limits, or treat it all as standard errors and use the rules for standard errors, or do I do choice 3: something else?

If you need any clarification let me know.