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.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Measurement uncertainty

**Physics Forums - The Fusion of Science and Community**