Uncertainty

Variable Definitions

$l\to$ length of pendulum

$g\to$ gravity

$T\to$ period of the pendulum

$\delta T\to$ uncertainty in the period

$\delta g\to$ uncertainty in the gravity

$\delta l\to$ uncertainty in the length

Uncertainty in the Measurement of g

The theory section shows that $g$ is found to be:

$g=\frac{4{\pi }^{2}l}{T^2}$

From this, the error can be found by:

${\left(\frac{\delta g}{g}\right)}^2={\left(\frac{\delta l}{l}\right)}^2+{\left(2\frac{\delta T}{T}\right)}^2$

This formulation is then used for calculations of the uncertainty and the accuracy necessary for keeping the error withing 1/10000. The error on the period is found from:

$\delta T=\frac{\sigma }{\sqrt{N}}$

where:

$\sigma =\sqrt{\frac{1}{N-1}\sum _{i=1}^N{(T_i-\overline{T})}^2}$