# Homework Help: Mechanical Resonance

1. Feb 8, 2008

### opuktun

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. Feb 8, 2008

### Andy Resnick

You are forgetting about harmonics: excitations at 2, 4, and 8 Hz will also excite a 16 Hz resonance.

3. Feb 8, 2008

### opuktun

Actually, 16 Hz is the fundamental frequency. Sorry, I did not clarify properly.

4. Feb 8, 2008

### TVP45

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.

5. Feb 8, 2008

### TVP45

By the way, except for that nutty Millenium Footbridge, bridges don't have undamped natural resonances unless somebody screwed up big time.

6. Feb 8, 2008

### opuktun

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

7. Feb 9, 2008

### TVP45

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!