Thu February 07, 2013 By: Pramod R

The period of oscillation of a simple pendulum is T = 2pi(L/g)^1/2 , L is about 10 cm and is known to 1 mm accuracy. The period of oscillation is about 0.5 s. The time for 100 oscillation is measured with a wrist watch of 1 s resolution . What is the accuracy in the determination of g ?

Expert Reply
Fri February 08, 2013
the only factors concerned with T are of L and g
thus we can write
g = K L/T2
where K is a constant
taking logatithm on both sides
log g = log K + log L - 2log T
and now differentiating
?g/g = ?L/L - 2?T/T
thus now relative error can be fod using their relative errors using the above equation.
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