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Homework Help: Mechanical Resonance

  1. Feb 8, 2008 #1
    Q: If a bridge has a natural frequency of 16 Hz and assuming that a battalion of soldiers marches across it, will mechanical resonance occur?

    Personally, I was quite unclear about the physical implication of "16 Hz". In my interpretation, I feel that to cause a mechanical resonance on the bridge, at a particular spot of that bridge, 16 cycles of march per second is required. But to make a spot to experience these 16 cycles per second is not very possible. Henceforth, I would like to check with the experts out there to see if I have made some errors in understanding.

    I would really appreciate some feedback. Thanks! :)
     
  2. jcsd
  3. Feb 8, 2008 #2

    Andy Resnick

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    You are forgetting about harmonics: excitations at 2, 4, and 8 Hz will also excite a 16 Hz resonance.
     
  4. Feb 8, 2008 #3
    Actually, 16 Hz is the fundamental frequency. Sorry, I did not clarify properly.
     
  5. Feb 8, 2008 #4
    Bridge designers commonly check for 2 Hz resonances as that is about what you can expect from foot traffic, even in cadence. I think Henry Petroski has a good section on that in one of his books, though I can't remember which. American Scientist also ran a piece on this within the past twenty years though that might well have just been Petroski again.
     
  6. Feb 8, 2008 #5
    By the way, except for that nutty Millenium Footbridge, bridges don't have undamped natural resonances unless somebody screwed up big time.
     
  7. Feb 8, 2008 #6
    Hi TVP45, thanks for the reply. Well, it's a theoretical question given in my tutorial. But I have not been touching my physics materials for five years? heh :P
     
  8. Feb 9, 2008 #7
    And, BTW, designers do screw up. Here in Pittsburgh, a major new bridge span (less than 20 years old) fell off its rocker Thursday. Ouch!
     
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