Questions About Electromagnetically Coupled Mechanical Oscillators

I have received a number of questions about the Oscillator problem. Before I post my answers, I want to emphasize that these answers are not official, but posted here for fairness.

In other words, the problems, as they are worded on the Problem Page, were written by me and in close consultation with the president of the organization (Greg Jacobs), and were subsequently approved by the board. The answers I give here have no such weight. If, in good faith, a team takes a creative approach, and learn their physics, they could be rewarded by the judges even if they disregard my answers here. That is fine. My experience is that juries love creativity, so long as the students understand the physics.

Q: According to the problem: “they must be coupled electromagnetically without any external power source.” So clearly, that rules out power supplies, but what about batteries?

A: The spirit of the problem is to not add any extra energy source to the system. If the purpose of the battery is to power some device other than a passive detector, than I would say no. If it is to temporarily store electrical energy, that was just produced, then it would probably be OK, but a capacitor would be more efficient.

Q: Is it OK to couple the oscillators just magnetically, or just electrically, rather than electromagnetically?

A: I think this should be fine, as long as you did not add any additional energy to the system and fully understand how it works.

Q: Once put in motion, the system comes to rest due to a variety of effects. Is that OK?

A: Yes. The problem forbids adding energy, so naturally frictional forces will eventually dissipate the energy. Obviously, you will want to minimize frictional forces if at all possible.

Q: Would it be OK to drive the system mechanically.

A: My vision was for this to be the classic problem of weakly coupled oscillators. The most common example is a playground swing set, where two identical pendulums are coupled with a flexible common bar. Here are some slides from a nice traditional lecture on the subject aimed at college juniors.

The driven oscillator is also a classic physics problem, but a different one than I had in mind. However, that does not necessarily mean that you could not do it instead, so long as it complies with the original wording. The most important thing is to have a strong grasp of the fundamental physics.

This is a difficult problem, but that is the point. We had an undergraduate student try to do this and not succeed within a semester. He wrote a nice paper about it, which you can see here. Just, as with all science, make sure you reference any prior work. And if you follow-up on his references, reference the original work.

My overall advice is to clearly and methodically break the problem down, and test each part separately. There is no rule against adding energy for hypothesis testing purposes. Then, when you understand each part, put the ideas all together. These parts might be:

  • Make a traditional coupled oscillator with mechanical coupling first, as some sort of proof of concept. Make sure it exhibits the expected behavior.
  • Make sure you understand how a strong magnet could affect a coil of wire. Do this by forming hypotheses based on the fundamental physics, and testing them one measurement at a time.
  • Make sure you understand how a coil of wire can affect a strong magnet. Again do this by hypothesis testing based on fundamental physics.

Also, keep in mind that the same things can be explained multiple different ways.

Traditionally you would start with Maxwell’s four field equations. If you do this, you must be able to explain them to someone without a prior knowledge of vector calculus. This is not a math competition, but a physics competition, so make sure you understand each one geometrically.

Alternatively you can explain some of the same things using the concepts of reference frames, Galilean transformations, and the Lorentz force. If you do this, again make sure that you can explain the physics fundamentally using pictures and diagrams.