The following question is about an experiment with the conical pendulum.//<![CDATA[ aax_getad_mpb({ "slot_uuid":"f485bc30-20f5-4c34-b261-5f2d6f6142cb" }); //]]>

I have measured the length [itex] l = 43\,cm [/itex] the radius [itex] r = 10\,cm [/itex], I have 3 measurement of the period with the same radius, where the measurements are

[tex] T= [1.288, 1.285, 1.301] s[/tex]

The uncertainties of the measurements are [itex] \Delta l = \pm 1\,cm[/itex], [itex]\Delta r = \pm 1\,cm [/itex] and [itex] \Delta T = \pm 0.02\,s [/itex].

I want to calculate the uncertainty in the measurement og [itex] g [/itex], when

[tex] g_i=4\pi^2\frac{\sqrt{l^2-r^2}}{T_i^2} [/tex]

Can I calculate the uncertainty [itex] \Delta g [/itex] by

[tex] \Delta g = 4\pi^2\frac{\sqrt{(l+\Delta l)^2-(r-\Delta r)^2}}{(T_i-\Delta T)^2} - g_i [/tex]

Where the expression [itex] 4\pi^2\left(\sqrt{(l+\Delta l)^2-(r-\Delta r)^2}\right)/(T_i-\Delta T)^2 [/itex] is the worst case scenario of the measuring [itex] g [/itex]. Is that correct?

If that is how I can calculate the uncertainty in [itex] g [/itex], is the relative uncertainty then

[tex] \frac{\Delta g}{g_i} \qquad \mathrm{or} \qquad \frac{\Delta g}{\overline{g}} [/tex]

Where [itex] \overline{g} [/itex] is the mean value. Which one is the correct one? The first expression has a relative uncertainty for each measurement.

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# Measurement uncertainty

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