Period error ?

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Answer 1 · 2016-08-28T19:55:55

$(dT)/T = -1/2(dg)/g$

Error propagation is easily handled using the $log$ transformation.
Given $T=pi/2sqrt(L/g)$ after tansformation reads

$log_eT = log_e(pi/2) +1/2(log_eL-log_e g)$

After deriving we have

$(dT)/T = 1/2((dL)/L-(dg)/g)$

supposing that $L$ is known with precision $dL approx 0$

so

$(dT)/T = -1/2(dg)/g$