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Measurement uncertainty

  1. Oct 15, 2005 #1
    The following question is about an experiment with the conical pendulum.
    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.
     
    Last edited: Oct 15, 2005
  2. jcsd
  3. Oct 15, 2005 #2

    HallsofIvy

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    Yes, calculating the value for the largest possible and then smallest possible values of l, r, and T gives the possible error for the function.

    The relative uncertainty is [tex]\frac{\Delta g}{g}[/tex].
     
  4. Oct 15, 2005 #3
    Well in the equation

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

    There is acctually an uncertainty of g, for every measurement [itex]\Delta g_i[/itex]. Should I say

    [tex] \frac{\Delta g_i}{g_i} \qquad \mathrm{or} \qquad \frac{mean(\Delta g_i)}{mean(g_i)} [/tex]?

    Where in the last equation I only have one value for the relative error. Im not quite certain of what to choose?
     
    Last edited: Oct 15, 2005
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