Physical Pendulum Period Analysis · USAPhO 2011 #A2

Physics · mechanics

Problem

A thin, uniform rod of length LL and mass M=0.258M = 0.258 kg is suspended from a point a distance RR away from its center of mass. When the end of the rod is displaced slightly and released it executes simple harmonic oscillation. The period, TT, of the oscillation is timed using an electronic timer. The following data is recorded for the period as a function of RR. What is the local value of gg? Do not assume it is the canonical value of 9.8 m/s². What is the length, LL, of the rod? No estimation of error in either value is required. The moment of inertia of a rod about its center of mass is (1/12)ML2(1/12)ML^2.
R (m)T (s)R (m)T (s)
0.0503.8420.2112.074
0.0753.1640.3021.905
0.1022.7470.3871.855
0.1562.3010.4511.853
0.1982.1150.5881.900
You must show your work to obtain full credit. If you use graphical techniques then you must plot the graph; if you use linear regression techniques then you must show all of the formulae and associated workings used to obtain your result.

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