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Why does movement vibrate at certain points?

  1. Oct 8, 2011 #1
    Referring to following images, when I jump up and down at 1/4 position on the bridge, I can feel the bridge vibrated a lot at this point, but when I jump up and down at 1/3 position on the bridge, I cannot feel any movement on the bridge at all.
    Does anyone have any suggestions on what cause the vibration on the bridge?
    Thanks in advance for any suggestions
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  2. jcsd
  3. Oct 8, 2011 #2

    Borek

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  4. Oct 8, 2011 #3

    NascentOxygen

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    All mechanical things have a natural frequency they will vibrate at, called resonance. This is a suspension bridge, is it? So it's fixed at the ends, but free to swing up and down along its length? There are likely to be be a few points along the length of something where the vibrations are greater, according to the distance from the ends, and the principal frequency of oscillation, etc. For a good example, search "Tacoma Narrows bridge" on google.
     
  5. Oct 8, 2011 #4

    AlephZero

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    As the other answers said, the general principle here is that the structure can vibrate at several different frequencies, and the shape of the vibration is different at each frequency. The simplest example of this is something like a guitar string, which can vibrate at frequences of 2, 3, 4, etc times the "fundamental" frequency. Google will find plenty of diagrams, and how to show this on a real guitar.

    To start the vibration of any particular mode, you have to apply a force (e.g. by jumping up and down) at approximately the right frequency, and you also have to jump up and down at a point that is going to move. You can't excite a vibration mode at the "nodal points" where the motion is always zero.

    It's possible that if you jump up and down at a different speed (say 2 or 3 times as fast, if you can do that) you will be able to "move" the bridge at the 1/3 point, by exciting a different vibration mode.

    However trying to go from those general principles to the specifics of your bridge is hard, for at least two reasons. One is that because of the suspension system the bridge is quite a complcated structure and it's not obvious what the vibration mode shapes will be. The second reason is that your own mass is probably not negligible compared with the bridge, and the complete system of "you plus the bridge" will have different modes of vibration from the bridge on its own, and also different vibration modes depending on where you are standing along the bridge.

    Probably the simplest way to investigate that would be to measure the vibrations of the bridge on its own, and then use a computer "add in" the effect of you standing on it at different points. Vibration engineers do this sort of thing routinely, but it's probably outside the capabilities of a school science lab, and needs a higher level of math to understand what you are doing even if you had the equipment to make the measurements.
     
  6. Oct 8, 2011 #5
    If the bridge is 24 m, could anyone please give me any suggestion on what frequency to jump up and down at 1/3 position will make this point into antinode?
    Thanks everyone very much for suggestions
     
  7. Oct 9, 2011 #6

    NascentOxygen

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    If you wanted to experiment, probably the best way to go about it would be to stand on the ground and rhythmically tap the swinging structure (try various locations) with a rubber mallet (or heel of a shoe) and lightly feel along the length for points of greatest vibration.
     
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