Examining Periodicity with a Goniometer

Gymnastic routines involve many types of repetitive motions. In graphs, repetitive motions tend to appear as sine wave functions. Sometimes, multiple sine wave functions must be added, in order to create more complex graphs. A form of advanced mathematics called Fourier analysis allows scientists to analyze oscillation which is more complicated than a simple sine wave.

The following graph is excerpted from The Science of Gymnastics: Volume 2 from Schottenbauer Publishing.

Discussion Questions

1. What is the smallest angle of contraction of the arm? What is the largest angle?
2. Counting from the bottom of the first trough, what is the amplitude of the first oscillation? What is the amplitude of the second oscillation?
3. Counting from the bottom of the first trough, what is the wavelength of the first oscillation? What is the wavelength of the second oscillation?
4. In the first two oscillations, what is the average frequency of oscillation?
5. What occurs at the end of the graph?

Additional graphs of oscillatory motion in gymnastics are available in the same volume, The Science of Gymnastics: Volume 2 from Schottenbauer Publishing. Similar physics data is also available in Volume 2 of several other lab manual series, including The Science of Athletic Training, The Science of Exercise Equipment, The Science of Yoga, Pilates, & Ballet, and more.

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Schottenbauer Publishing

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Force & Acceleration in Gymnastics

Common gymnastics events can demonstrate the relationship between force and acceleration. Consider the following graphs, excerpted from The Science of Gymnastics: Volume 1 from Schottenbauer Publishing. Although both graphs demonstrate a similar phenomenon, these data were recorded on separate occasions.

Discussion Questions

1. What is the maximum force in the first graph? The second graph?
2. In the first graph, how long is the person in the air for each jump?
3. What is the maximum acceleration in the second graph (assuming that the x axis is vertical)?
4. In the first graph, where does the person begin? (a) On the floor, (b) On the force plate.
5. In the first graph, where does the person end? (a) On the floor, (b) On the force plate.
6. In theory, which requires more force? (a) Stretch Jump, (b) Bounding. 
7. In the first graph, which shows the most force? (a) Stretch Jump, (b) All Bounds, (c) Final Bound.
8. In the second graph, which shows the most force? (a) Stretch Jump, (b) All Bounds, (c) Final Bound.
9. In theory, which requires more acceleration? (a) Stretch Jump, (b) Bounding. 
10. In the second graph, which shows the most acceleration? (a) Stretch Jump, (b) All Bounds, (c) Final Bound.
11. In the second graph, what is the maximum height of the bounding?
12. Do these two graphs show similar technique? If not, describe the differences in words.

Additional graphs of force and acceleration, are available in the same volume, The Science of Gymnastics: Volume 1 from Schottenbauer Publishing. Similar physics data is also available in Volume 1 of several other lab manual series, including The Science of Athletic Training, The Science of Exercise Equipment, The Science of Yoga, Pilates, & Ballet, and more.

Additional Information

Schottenbauer Publishing

Free Education Resources

The Science of Gymnastics: Exploring the Possibilities!

The science and math of gymnastics are topics of new books from Schottenbauer Publishing. Presenting data from real moves collected by the science writer and publisher M. Schottenbauer, Ph.D., these books bring the "high tech" end of gymnastics to audiences everywhere!

In these books, students can enjoy learning about common moves from gymnastics, including floor, vault, high bar, rings, parallel bars, and pommel horse. One series of books, written for elementary school students, focuses on geometry. Two series of science books feature graphs and data; these illustrate common mathematical functions, plus a variety of concepts from physics and biophysics. The science books can be integrated into classes such as math, physical science, physics, physical education, and health, anywhere from 7th grade through high school, as well as some introductory college and university classes. 

The books which include gymnastics include the following:

Geometry Workbooks

• The Geometry of Gymnastics
• The Geometry of Summer Olympic Sports 

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Gymnastics
• Volume 1: Force & Acceleration
• Volume 2: Biophysics
• Volume 3: Video Analysis

Anthologies of 28 Graphs

• The Science of Gymnastics
• The Science of Summer Olympic Sports

These books are complemented by a series of science books on other popular sports topics, including Olympic sports, athletic training, exercise equipment, yoga, and more. Topics related to gymnastics include:

Geometry Workbooks

• The Geometry of Yoga
• The Geometry of Ballet

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Athletic Training 
• Volume 1: Force & Acceleration
• Volume 2: Biophysics
• Volume 3: Video Analysis
• The Science of Exercise Equipment 
• Volume 1: Force & Acceleration
• Volume 2: Biophysics
• Volume 3: Video Analysis
• The Science of Yoga, Pilates, & Ballet 
• Volume 1: Force & Acceleration
• Volume 2: Biophysics
• Volume 3: Video Analysis

Anthologies of 28 Graphs

• The Science of Physical Fitness
• The Science of Dance & Ballet
• The Science of Yoga

Most of the books above are available in both English and German translation. The books pertaining to the geometry of Olympic sports are also available in 15 world languages. 

The same publisher offers similar books on additional popular topics, including sports, transportation, construction, environment, music, entertainment, and general physics. All of these book series are available in several formats and languages, including the following:

Geometry Workbooks

• Print & E-Book Editions
• Available in English & German
• Olympics Books Available in 15 Languages

Graphs & Data for Science Lab: Multi-Volume Series

• Print Editions
• Available in English & German

Anthologies of 28 Graphs

• Print Editions
• English Only

Additional Information

Schottenbauer Publishing

Free Education Resources

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MusicaNeo Digial Sheet Music

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Unbeatable Specials

With Kindle Unlimited ($9.99/month) at Amazon.com, you can read all e-books from Schottenbauer Publishing for no extra charge! Amazon offers Free 30 Day Trials of Kindle Unlimited. With this deal, trial members can read all Schottenbauer Publishing e-books free! This includes all the geometry workbooks, plus "The World in a Graph," "Alphabets of the World," textbooks on the science of music, all the e-book puzzles, and the educational novels by M. Schottenbauer, Ph.D.