A pendulum of length has small-angle period with

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Computational Physics, Ch Seeing the answer: plots that can be trusted

Problem

A pendulum of length L=1.00 mL=1.00\,{\rm m} has small-angle period T0=2πL/g=2.0071 sT_0 = 2\pi\sqrt{L/g} = 2.0071\,{\rm s} with g=9.8 m s−2g=9.8\,{\rm m\,s^{-2}}. Periods are measured at five release amplitudes θ0\theta_0, with each period repeatable to within σ=0.0005 s\sigma = 0.0005\,{\rm s}: θ0=2∘: T=2.0073 s\theta_0=2^\circ:\ T=2.0073\,{\rm s}; 5∘: 2.0081 s5^\circ:\ 2.0081\,{\rm s}; 8∘: 2.0095 s8^\circ:\ 2.0095\,{\rm s}; 11∘: 2.0117 s11^\circ:\ 2.0117\,{\rm s}; 14∘: 2.0146 s14^\circ:\ 2.0146\,{\rm s}. Someone plots TT against θ0\theta_0 with the vertical axis autoscaled tightly to the data, running from 2.007 s2.007\,{\rm s} to 2.015 s2.015\,{\rm s}, and writes: "the axis spans only the range the data occupy, so it shows exactly what happened: the period rises sharply with amplitude, and the small-angle formula fails badly." ((a)) Identify the misleading practice in this figure. ((b)) Say what a repaired figure would actually support, using the size of the change relative to σ\sigma.

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