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27 April 2013

Pendulum Waves (Not So)

Before I start, I would like to thank my ever-supportive father, who spend so much effort for making this beautiful wooden frame. He is a skilled craftsman (carpenter) who inspired me partly to become an experimental physicist.



Now, about this video:

As I have mentioned, it is a demonstration of a so-called pendulum wave. I was very much impressed by the pattern of repeating oscillations shown to me by a friend not too long ago, so one day I decided: why not build one? After all, you never truly know something until you design and test it yourself - it is the heart and reason why we do experiments in science.

So I bought 20 fishing leads as bobs, they are graded (as casted on their surface) "3". I am not entirely sure what it meant, but I presume it is an index of weight. However, simple mechanics dictates that the period of oscillation in a pendulum is independent of the bob's mass. Hence, slight difference of mass between the bobs should not matter in a synced-oscillations as it would not affect its "swinging frequency".

I used a series of plastic zip-strips as pivots for the pendulums. 16 bobs are arranged in successive 0.5 cm increment, sharing pivots with another.

Comparing with available pendulum waves demonstration, this video appears to exhibit a failed example. Initially, the collective oscillation shows pattern resembles a wave-like motion, but because there is a small difference in frequency between the successive bobs which results in de-phasing after a few cycles of oscillation, which collectively shows a quick decay from a wave-like pattern into seemingly random movements.


However, it is important to note that this "failure" was not unpredicted for three reasons:

1. The bobs are sharing the same pivot with each other. i.e. there is only one continuous string that ties from one-end to another end of the wooden frame. As such, the component mechanical forces acting on each bob during their individual oscillation could perturb the adjacent bob - creating a dynamic system.

2. Successive bobs are arranged in a linear increase of length, that is the height difference between successive bobs are constant at 0.5 cm. If the frequency of swinging is critically dependent on the bob length, i.e. tiny difference such as 0.5001cm from one bob to another, then we can expect the synced-movement to decay rapidly as time goes on.

3. The string that is holding the bobs is very thin. At times, some bobs twist while swinging (we call torsion) which dampens the oscillation for each pendulum.


Below is a video of a simulated "pendulum wave" if we vary the bob lengths linearly. A good friend of mine used MATLAB(TM) to simulate this 19-bobs movement, and we can see obvious de-phasing of the synced-oscillation after the first mode at about 00:30 video time. Note the pattern of the mode decay is similar to my video earlier. 



Therefore, we speculate that the supposedly "ordered" displacements between the bobs is critically dependent on the linear increment in frequency of each successive bobs instead of the length.


2 comments:

Li Voon Loke said...

If you repeat the experiment using bobs of different mass, you would obtain the same result (say everything else is the same as the first experiment ) ? Seems really counter-intuitive, as with most physical concepts...
And as for the wave, is the pattern predictable? It doesn't look random to me.

Andrew.C said...

Yeap, using bobs of different mass shouldn't significantly affect the oscillating frequency.

You're right! counter-intuitive as it is, when we perform something called "dimensional analysis" on the frequency we will realize frequency's unit, which is [time]^-1 is did not mention [mass] in it. As such, oscillation of a pendulum should not be affected by the pendulum's mass.

It is important to realize this concept is similar to why all object falls under earth's gravity in the same rate independent of their masses.

***

Yes the pendulum waves looks "random" because when we view it with only limited bobs. See, as time goes on, the number of "waves" increased, and that require more bobs to show the increment of waves. Since we have only 16, the wave pattern slowly disappears into "random-like" motion.