The time period of small oscillations of a simple pendulum is given by

PHYSICS · Subjective · A Level · Physics · Measurements and their errors · Measurements and their errors

Problem

The time period of small oscillations of a simple pendulum is given by T=2πLgT = 2\pi\sqrt{\dfrac{L}{g}}, where LL is the length of the pendulum and gg is the acceleration due to gravity. A student measures L=1.000 m±0.005 mL = 1.000\,\text{m} \pm 0.005\,\text{m} and g=9.80 m s−2±0.05 m s−2g = 9.80\,\text{m\,s}^{-2} \pm 0.05\,\text{m\,s}^{-2}. (a) Derive an expression for the fractional uncertainty in TT in terms of the fractional uncertainties in LL and gg. (b) Calculate the numerical value of TT and its absolute uncertainty. (c) Present the final value of the time period with its uncertainty, rounded according to the rules of significant figures.

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