Pendulum Conundrum

A classmate and I were mulling over pendulums on the train ride last night and couldn’t come to any conclusion. We were discussing how mass as a variable effects two pendulums. Initially, my response was that a more massive pendulum would rise to a higher point once released (if two pendulums of differing masses were released from the same height) because it has greater PE, but then we got confused because it also takes more energy to keep it swinging. So then it also made sense for both pendulums to reach the same height and have the same period with every oscillation.

Since we couldn’t come to any conclusion, I went home and played around with some homemade pendulums. I constructed one with some gift wrapping ribbon and one fork and another with gift ribbon and five forks. Attached is a slide show and commentary of what I found. I pretty much observed both phenomena of the two forks at same heights with same periods as well as two forks with same periods but different heights. Then I coupled the two pendulums just for kicks.

My husband Keith got home from work as I was curled up nearly under the sink in the bathroom trying to take pictures. Oh, Physics!


One response to this post.

  1. Posted by Becky McCoy on November 23, 2008 at 6:39 pm

    A response from my Physics professor at TC:

    Interesting! Theory is, I think, that, without friction, a pendulum will continue to rise to same height from which it started, so 2 pendulums, no matter what the mass, will rise to same height if started at same height. In fact, even if one pendulum has shorter length, and thus shorter period, it will rise to same height if started from same height. With friction, it's more difficult to predict. But your experiments seem pretty convincing – I'd say the explanation for what you found is that since the two pendulums have roughtly the same "size" and the same speed, the frictional forces on them due to the air will be about the same, and since the distance they travel is about the same, the frictional work will be about the same and thus the amount of energy lost to friction will be about the same for each swing. But the larger mass pendulum will have a much larger energy (GFE & KE), so the larger mass will lose a smaller percentage of its energy on each swing. And that means it will "lose" less height at the end of each swing. (If change in mgh is about the same for both, but m is greater for larger mass, then change in h must be smaller.) So I guess it's more accurate to say that the smaller mass loses height faster, rather than that the larger mass swings higher – since both swing lower on each swing.

    Another way to think about it might be that the friction is about the same for both pendula because they have about the same area exposed to the air, but friction affects the smaller mass to a greater extent – just the way air friction would affect a falling real feather much more than a falling feather made of lead.


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