A simple pendulum has length

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Uncertainty in measurement

Scientific Computing for Physicists, Ch The uncertainty of a simulated number: inputs, sensitivity and correlated output

Problem

A simple pendulum has length L=0.750±0.003 mL = 0.750 \pm 0.003\,\mathrm{m}, an epistemic uncertainty in a fixed length, evaluated Type B from the tape measure's scale. Its small-amplitude period is T=2πL/gT = 2\pi\sqrt{L/g}, with g=9.8 m s−2g = 9.8\,\mathrm{m\,s^{-2}} treated as an exact constant. ((a)) Compute TT at the central value of LL. ((b)) Propagate the uncertainty in LL linearly to obtain uTu_T.

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