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I am looking for simple experiments that students can perform as projects for an ODE course. For example experiments related to Newton's law of cooling or dynamics of a pendulum. What other topics would you suggest? Do you know of a text with such a perspective?

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Are you okay with computer simulations, or do they have to be real lab experiments? –  user53153 Jan 3 '13 at 5:04
My preference is real physical experiments. Simulations will be of second interest. Having both will be a plus. –  Maesumi Jan 3 '13 at 5:10
You might find this instructive, whatever you choose Circuits, Tanks and Mathematical Models. I would think that you want to show the utility of using closed form solutions (manual crank), using a CAS, using numerical methods and using experimental methods. You might be able to use simple falling bodies from a height as those meet the criteria of quick setup and easy collection of data. Have fun! Regards. –  Amzoti Jan 3 '13 at 5:26
You might want to look at Harvey Mudd and CODEE Digital Library, ODE Architect and ODE Toolkit. Regards -A –  Amzoti Jan 3 '13 at 5:44
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1 Answer

up vote 3 down vote accepted

I would suggest to consider projects about ODE and not about physics (or anything else).

However, if you insist, you can ask your students

  • to grow a colony of bacteria to confirm an exponential law of growing (I don't think it is a good idea to deal with radioactive decay, but who knows...)
  • to measure frequency of the pendulum motion (and see when the linear approximation starts breaking)
  • to build a Zeeman's catastrophe machine if you'd like to talk a little about bifurcations
  • to construct electric circuits (limit cycles can be effectively modeled with this approach, not only a simple harmonic motion)
  • to validate the Lanchester's combat model by simulating some kind of "war"
  • following Gause and using two types of bacteria your students can validate the theoretical results of the competitive exclusion
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Could you elaborate on "consider projects about ODE and not about physics"? What issues do you see? By the way projects including any actual biology will require "institutional approval" and are likely to be to risky/questionable for a simple start-up. –  Maesumi Jan 3 '13 at 19:02
@Maesumi This is my personal opinion, you can just ignore it. I agree about biological experiments, however, the same is probably true for any nontrivial physical of chemical (or whatever else) experiment coming beyond simple harmonic oscillator. –  Artem Jan 3 '13 at 20:43
Thanks. The Zeeman's machine is interesting and looks doable even though not a simple pendulum! –  Maesumi Jan 3 '13 at 21:57
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