A pendulum of length

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

Measurement and Method, Ch Repeated readings: scatter, the mean and the standard error

Problem

0.750\,\mathrm{m}

, swinging with amplitude about

4^\circ

, is timed for twenty complete oscillations using a stopwatch resolving

0.01\,\mathrm{s}

. Eight timings are recorded (s):

24.62,\ 24.58,\ 24.65,\ 24.60,\ 24.63,\ 24.59,\ 24.61,\ 24.64

. ((a)) Calculate the mean time for twenty oscillations,

\bar t

, and the sample standard deviation

s

. ((b)) Calculate the standard error of the mean,

\sigma_{\bar t}

. ((c)) Divide by twenty to find the period

T_{\rm p}

per oscillation with its standard error, and write the result in house form, stating

N

. ((d)) Name two effects that this uncertainty does not include, and say briefly why repeating the timing further would not remove them.

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