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(Science background: A pendulum has a resonant frequency and will swing noticably higher if 'driven' at or near its resonant frequency. The resonant frequency varies with the length and weight of the pendulum).
I was walking behind a woman earlier today whose ponytail resonant frequency and walking
cadence were so perfectly correlated that her (large) ponytail swung left and right up to the horizontal with each step she took. This then is an idea for a device (or perhaps an add-on function for an existing device, such as a pedometer) which will use as input parameters data on your walking cadence and the length and weight of your ponytail and sound an alarm if you are in danger of approaching a walking cadence/ ponytail resonance synchronisation. You can then take remedial action, such as walking faster or getting a haircut.
Suit of swing
Suit_20of_20swing
As a ponytailless pedestrian, jealousy has inspired invention. [Worldgineer, Jul 31 2007]
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they're great as weapons if you swing around fast enough. |
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I'm not quite sure what you're getting at here, h. |
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btw did you ever see the pic I posted for you over at M? |
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I thought they always bobbed in resonance? |
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[po] sorry - missed that
[bigsleep]
Yes, good point. Perhaps this
should be repurposed as a device to allow
the wearer to maintain a chosen level of
ponytail resonance with their gait. |
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[Fuzzy Logic]: It's the length of a pendulum that determines it's frequency, not it's weight. (At least that's what I remember...?) |
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<useles fact #5302>The classic c64 game Yie Ar Kung Fu II had an enemy called Yen Pei and his special weapon was his Iron Pigtails.</uf> |
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pointless and stupid (make that daft
actually) = my total
approval + |
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Actually, by choosing a pace at one's ponytail resonant frequency, kinetic energy could be stored in the ponytail, which would then be imparted to the walker on the next swing. |
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If the wearer wore two of those bobbly-
things in her ponytail, one near the end
and one somewhere mid-way, then the
ponytail would become a complex
pendulum and would not have a resonant
frequency. |
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/It's the length of a pendulum that determines it's frequency, not it's weight/ |
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No, it isn't. At least for a classical
pendulum, the weight on the end of the
string has no effect on its frequency. |
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Simple gedanken experiment to prove
this: set up two identical pendula side
by side and set them swinging in synch.
Now add a drop of liquid glue between
the two bobs as they swing side-by-
side. Do they change speed? Of course
not. Now let the glue set. Does this
change their speed, of course not. Now
replace the two adjacent strings with a
single one of the same length. Does
this change the speed? No. So you have
doubled the mass of the pendulum
without altering its frequency. QED. |
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I stand corrected. The mass term cancels out for a simple pendulum. |
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Nice gedanken experiment [Maxwell] - for some reason I can't clearly remember though, the "simple harmonic motion" equations only work for pendulums with very small amplitudes. For a violently swinging ponytail, I think mass does come into the equation. |
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Actually - you might be right. My old high school physics project was to measure small 'g'. To do so most effectively I suspended a pendulum the entire height of the stair well (4 stories). If I remember correctly, this was to minimise the approximation based on trig. of triangle vs circular arc. |
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Somewhere, mass did come in to the equation. |
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I'm thinking that we're in danger over analysing here. |
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<tabloid scandal>
Halfbakery in pointless pedanto-science SHOCK! - Pictures inside
</tab scandal> |
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I think mass stays out of the equation (I suppose at some point one of us should look it up). Go back and re-read [Max]'s comment, but replace it with a big swing. |
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I always thought they did this on purpose. |
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+ as long as I can have bells attached... |
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//Somewhere, mass did come in to the
equation// Mass becomes relevant in
two contexts: |
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(a) when factoring in "losses" such as air
resistance or friction at the pendulum's
pivot etc. In these cases (and
particularly when the swing is large),
small masses are proportionally more
affected than large ones. |
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(b) when the mass of the "bob" is small
compared to the mass of the "string".
The simple calculation assumes that the
string (or whatever) has negligible
mass; again, this doesn't work when the
mass of the bob is very small. |
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For a ponytail, it is indeed more
complex. The mass is distributed along
its length rather than at the end; the
ponytail is flexible to an extent; and the
root of the ponytail is pretty much fixed
in one direction (determined by the
direction of hair growth and the way the
ponytail is gathered). In some respects,
therefore, the ponytail is midway
between a simple pendulum and a ruler
twanged on the edge of a desk. |
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Period of swing (simple pendulum) is two pi root L over g. (the mass cancels out from the equations that you have combined to get this one.) But, whilst I agree that the classic three-plait pony tail is a complex pendulum in theory, the fact remains that it will have a resonant frequency resulting in the effect that so disquieted hippo. Personally it is not a problem from which I suffer (disquiet - not resonance, though not that either) and so I welcome any inventions that make body parts swing wildly and discourage any that aim to prevent same. |
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Picturing a flouncing ponytail, it seems in my mental simulation that is is more like a continuously cracking whip (Split ends whistling with speed, roots clamped tight under elastic) than a pendulum, probably because the weight is evenly distributen. |
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//because the weight is evenly
distributen// Das ist eine Deutche
geponytailen, nein? |
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The German for ponytail is even better that that: "Pferdeschwanz" (according to Babelfish). |
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Bun for the notion, even though I like it when my ponytail and gait synchronize in a way that (some might consider positively preposterous but) makes me feel positively Marlo-Thomas-ish. |
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It occurs to me, a frequent ponytail wearer, that the way to quickly dispell the pendulum effect is to simply lower the ponytail on the back of your head. If it bothers you so much. I rather think that woman was pretty proud of her high-flying hair. |
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Can we harness the power of the ponytail? Perhaps a ponytail-powered gym? |
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