3A10.40 • Pendula: Mass-Period Independence

Location: Cabinet 5

Photo shows the demonstration used at the University of Texas at Austin.

Concepts Conveyed:

For simple harmonic motion, the angular frequencies, and thus the periods, of the pendulums depend only on their length and their acceleration near Earth's surface due to gravity.
Lightly damped pendulums with bobs of different masses will all have the same periods of oscillation at least initially.
The pendulums can be released at different, small angular displacements from one another since the angular displacement is also independent of the frequency in the small-angle approximation. This makes observing the period’s independence of the mass somewhat more difficult, however.
Damping can be seen to occur in this demo, affecting the amplitude and frequency of the foam ball bob much earlier, the wood ball bob’s later, and the steel ball bob’s only slightly.

Instructions / Notes:

The masses of the bobs were measured to be 229.21 ± 0.10 g (steel), 35.26 ± 0.05 g (wood), and 2.59 ± 0.05 g (foam).
The lengths of the pendulums from the bottom of the cross bar to the center of the balls were measured to be 38.58 ± 0.09 cm (steel), 38.65 ± 0.05 cm (wood), and 38.7 ± 0.1 cm (foam).
Use the initiator stick to displace the pendula, then remove quickly.
Observe the initial oscillations of the pendulums.

Demo Staff:

Last updated on March 24, 2025