1) The document uses concepts of damped oscillation to explain why the character Swinger Girl from the cartoon Recess never succeeded in swinging over the bar of the swing set throughout the 4+ year run of the show. 2) A swing oscillates in simple harmonic motion like a pendulum, but additional opposing forces like friction, tension, and drag dampen the oscillations over time, decreasing the amplitude and frequency of the swings. 3) When accounting for these dampening forces as well as the limited energy of an elementary school child, it would have been nearly impossible for Swinger Girl to generate enough momentum in her swings to make it over the top of the bar within a typical 15 minute recess

1. The Reasons Why Swinger
Girl Never Made it Over the
Bar
Explained using the concepts of Damped Oscillation!

2. Some of you may be familiar with the Disney
cartoon...
RECESS!!
http://o.canada.com/technology/gaming/disney-infinity-5-disney-characters-that-are-a-perfect-fit-for-the-game

3. In the show there is this
character named, Swinger Girl.
For those who aren’t familiar
with the show, Swinger Girl’s
mission is to swing over the
swing set bar and loop around...
http://vignette4.wikia.nocookie.net/recess/images/4/47/216462_1239072689503_full.jpg/revisi
on/latest?cb=20110422213830
However, she never did throughout this show (which aired for 4+ years!)...

4. So how can we explain those
4+ years of failures? If we
apply physics to this we can
figure out why!

5. First off...
● We need to see that:
o A swing is
basically a
simple
pendulum whose
motion is
periodic and has
simple harmonic
motion

6. If this were a simple pendulum, all she
would have had to do is start at a height
close to 180° above the swing set and she
would have succeeded as a perfect
pendulum oscillates indefinitely.

7. However!
There is more than
just that! We need to
take into account the
forces that are one the
swing!
http://www.gettyimages.ca/detail/photo/swing-
royalty-free-image/119090965?Language=en-GB
Tension Force

8. Applied Forces:
● Inertia force
● Forces due to kinetic energy
Opposing forces:
● Tension
● Friction:
o between object and the
chain
o between the individual
chain links when the
swing moves
o between the chain and the
rigid support
● Drag Force: forces that an
object experiences when
moving through a medium (eg.
air) with a velocity
Tension Force

9. One reason for her
failure was that there
were too many forces
acting against her...
Tension Force

10. Simple harmonic motion is modified by
dampening forces and results in:
● The exponential decrease in the amplitude of
the oscillator over time
● An oscillation frequency of a undamped
oscillator larger than the oscillation
frequency of a damped frequency

11. In turn, the simple harmonic oscillator loses energy (provided by
Swinger Girl).
1. As the system loses amplitude, so does it energy, Esimple harmonic
motion= Amplitude
2. To move against the drag force, work is done by the system and
uses energy.
3. The dampened oscillator takes more time to complete a cycle
because it slows down
Moving against the drag force is like
being splashed in the face by air from
the front and the back with your whole
body (but in a less dramatic way of
course!). Since energy is used in forms
like this, the swing doesn’t move like a
simple harmonic oscillator.
http://media.giphy.com/media/tlijLlismllTy/giphy.gif

12. This makes this an underdamped
oscillation, meaning that the amplitude
decreases exponentially with time due to the
drag force.

13. As the system continues to oscillate, a fraction
of the energy will be converted to other types of
work with each oscillation. This will continue
until the system loses all of its energy and
stops.

14. Now that we know the effects of undamped
oscillation, other frictional forces and taking
into account the total energy that a little
elementary school girl has and how fast she can
“pump” all that energy into pushing herself
over a swing set in 15 minutes. Its basically
impossible for her to swing over the swing set
all by herself (based on damped oscillation,
there are other factors too).

15. However!
I won’t say that this is an impossible feat. It is
still possible,
(https://www.youtube.com/watch?v=OZ9GuJybU0E). If she had
an external force pushing her and different
equipment it could be possible, but that’s a
different chapter for a different time!

16. Thanks! I hope this helped! :)