Schottenbauer Publishing

Wednesday, October 7, 2015

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 TrainingThe Science of Exercise EquipmentThe Science of Yoga, Pilates, & Ballet, and more.