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Masting the Playground Swing-set with Physics

Physicists Chiaki Hirata, Shun’ichi Kitahara, Yuji Yamamoto, Kazutodshi Gohara, and Michael Richardson offer new insights into the physics of the perfect swing.

(In (loose) couplets.

Back…forth, back…forth -- )


(We all remember that perfect ride on the swingset --

Back…forth, back…forth, back…forth, back…forth, back…forth, back…forth, back --)

Slightly rusted steel squeaking in the soft wind;

the seat was wet with droplets of morning dew.

It beckoned to you,

and you rushed over.

Children have been chasing the high since on the island of Crete 1400 B.C.E.,

and most recently with the modern playground swing since the turn of the 20th century.

Several curious children grew up to be keen physicists with an

unsatisfied urge to understand the mystique of that floating feeling.

And for half a century between 1970 and 2020, Physicists have used

an understanding in Classical Mechanics theory to explore the science of the playground swing:

“A coupled oscillatory system” --

The swing (object) and the swinger (human).

(-- Three good kicks

and you’re off.

Timing each kick with the creaks, your core rocks

with the rhythm bringing you higher.

And then, you see

over the trees.

You hear the wind whisper,

“Woah, now look at you go!” )

There are two models that describe the mechanics

of the coupled oscillatory swing system:

the fixed-frequency model --

the torso moves to its beat --

and the square-wave model --

torso and swing coupling.

This model from Japan

brings the two together.

Smooth upper body movement that is

fluidly adapting to the swing.

Central to their model is two parameters (12):

alpha (ɑ) and omega (ɷ) --

the initial lean back for the kick, and

frequency of the leans, respectively.

The model assumes the swing is a uniform,

rigid body, made of a chain and a seat.

in the hips and knees are two degrees of freedom

that cause the model results to vary (-- forth, back --).

Resonance between swinger’s rock and swing

results in a gain in the height of the swing.

When moving as fast as 12 mph,

“one can feel the airflow through hair and on the face.”

Thus, the model also contains the friction parameter K,

which is made proportional to the square of the velocity.

The group then ran an experiment with 20 participants

to see if the results of their model matched a real-life setting.

Resonance between the model and experiment showed that perfecting the timing

of the lean -- it’s start and frequency -- were indeed central to getting maximum gain.

(For a moment you fly

as if dressed in feathers.

The next, you fall to the ground with all those

oddly-shaped rocks in your pocket.

You dust yourself off, then -- forth, back --

you’re back to do it all again.)

To read the entirety of this research, please refer to this link.

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