Graphs of harmonic oscillation and rotation appear very similar when charted on graphs. Harmonic oscillation consists of a mass which moves back and forth in repetitive motion on one axis. Rotation consists of a mass in circular motion around a central point. On a graph, the mass appears to be moving back and forth in repetitive motion on each of two axes.
Consider the following graphs, excerpted from books by Schottenbauer Publishing.
Discussion Questions
- Which graphs show harmonic oscillation?
- Which graphs show circular motion?
- Describe the relationship between x and y components in circular motion.
- Using these graphs, describe at least one similarity between harmonic oscillation and rotation.
- Using these graphs, describe at least one difference between harmonic oscillation and rotation.
Over 8,000 graphs from Schottenbauer Publishing provide real-life topics for student learning, including sports, transportation, construction, environment, music, entertainment/toys, and general physics.
Celebrate graphs with memorabilia from Zazzle! Colorful graphs from Schottenbauer Publishing are featured on these mugs, magnets, keychains, & postcards. A direct link is included below:
A variety of other STEM education collections are also available from Schottenbauer Publishing on Zazzle, which features regular sales on most items.
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What is the meaning of the term "origin"?
According to Dictionary.Reference.com, there are up to eight meanings, two of which are mathematical. The first of these is commonly found in elementary and post-secondary graph-reading skills, while the second (not included here) pertains to more advanced math.
To answer the above question using the common math definition: Every graph in a Cartesian coordinate system has an origin, which is defined as the intersection of the axes.
Placement of the origin can dramatically affect the presentation of the graph. Consider the following two graphs, which present the same data, but with different origins.
Discussion Questions
- For each graph, identify the following coordinates: (a) Initial Position, (b) Final Position, (c) Minimum Position, and (d) Maximum Position.
- What is the relevance of the origin in each graph (if any)?
- Which graph is more useful for visual analysis?
- Do any additional differences exist between the graphs? If so, what difference(s) exist?
- Do the graphs contain any distortion of data, due to method of collection? If so, what is the distortion? How might the distortion be corrected?
Now, consider a different meaning of "origin." This definition is not mathematical; rather, it refers to "the first stage of existence," or the creation of an entity.
Using this definition, what are the origins of the over 8,000 graphs of sports, transportation, construction, environment, music, entertainment/toys, and general physics from Schottenbauer Publishing?
Created by M. Schottenbauer, Ph.D. in laboratory settings, these graphs represent several years of intermittent data collection and graphing activity. The objects studied in the graphs consist of the properties and motion of toys, hobby equipment, household objects, musical instruments, and sports equipment, measured and manipulated by the author. All music and sports activities were conducted by the author, including performance samples on 33 musical instruments and exercises from over 30 sports. Videos of some of these activities are available on YouTube.
Blogs with Free Graphs
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What is more entertaining than learning science and math from the real world? Combining STEM education with fun, The World in a Graph by M. Schottenbauer, Ph.D., is a curiosity piece for educators and students alike. This concise anthology of 28 graphs presents a spectrum of interesting topics from sports, transportation, construction, environment, music, and entertainment. Graph topics, in the same order presented in the book, include:
- Sports
- Baseball
- Tennis
- Ice Hockey
- Snow Skiing
- Running
- Walking
- Biking
- Weightlifting
- Gymnastics
- Track & Field
- Figure Skating
- Ballet
- Transportation
- Wheels
- Cars
- Planes
- Trains
- Boats
- Construction
- Material Strength Testing
- Electricity
- Indoor Lighting
- Environment
- Natural Light
- Natural Water
- Wind
- Entertainment
- A Moving Block
- A Falling Domino
- A Rolling Marble
These topics provide a rich selection of concepts from physical science and physics education, including:
- General Mechanics
- Force
- Friction
- Material Strength
- Collisions
- Energy
- Momentum
- Free-Fall
- Projectile Motion
- Motion on a Plane
- Motion on an Inclined Plane
- Rotational Motion
- Harmonic Oscillation
- Electromagnetism
- Electric Potential
- Current
- Power
- Light
- Acoustics
- Biophysics
- Electromyogram (EMG)
- Range of Motion or Joint Angles (Goniometer)
These topics provide a variety of important concepts from math, including the following types of mathematical functions:
- Math Topics
- Straight Line
- Curve
- Parabola
- Exponential Function
- Sinusoidal Function
- Integral
- Derivative
- Damping Function
- Random Error
The World in a Graph by M. Schottenbauer, Ph.D. is available from multiple internet retailers, in paperback and Kindle digital editions, as well as wholesale.
Schottenbauer Publishing offers a wide selection of books, featuring over 8.000 graphs from sports, transportation, construction, environment, music, entertainment, and general physics. Additional information is available on the blog Science and Math Education.
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