A group times ten swings of a pendulum sixty times over 45 minutes while a nearby…

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Data analysis and model fitting in the laboratory

Measurement and Method, Ch Models, idealisation and what a measurement is evidence for

Problem

A group times ten swings of a pendulum sixty times over 45 minutes while a nearby heater cycles on and off, slowly warming the room and the string. Plotted against reading number, the sixty period values show a slow upward creep of about

0.0007\,\mathrm{s}

over the run, on top of scatter with sample standard deviation

s \approx 0.0006\,\mathrm{s}

. Their report reads: 'The bootstrap makes no assumption about the shape of the distribution of our readings, so we resampled the sixty periods 2000 times with replacement and report

u(\bar T) = s/\sqrt{60} = 0.00008\,\mathrm{s}

.' ((a)) Find the error in this reasoning. ((b)) Name the diagnostic that would have revealed the problem before the bootstrap was run.

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