Part 1: Calculations
There may be many things going on around you that are periodic that you do not even realize!
Perhaps there is an old grandfather clock in your house, with a pendulum swinging back and forth inside. That pendulum is one example of periodic motion that can be graphed using trigonometric functions. How about the hands on the face of that same grandfather clock? They repeat the same pattern every 12 hours, 60 minutes, and 60 seconds. The tides rise and fall in a periodic fashion, the planets travel around the sun, and the earth rotates on its axis. These are all examples of periodic motion!
Your assignment is to choose an object, or event, around you that can be represented by trigonometric functions, then complete the following tasks.
Note: If you are having trouble finding an object or event to use, feel free to email your teacher to discuss possible options.
Record your event through a series of photographs, a video or another appropriate method. (For example, if you are using an oscilloscope, include a photo or video of the sound wave, and a copy of the audio file that you are measuring; If you are using a website like this one:
https://astro.unl.edu/, include a screenshot, or create a video using Jing).
2) Record the starting yvalue of your object or event (when x = 0).
3) Find the period of the object or event.
4) Find the maximum and minimum yvalues. You will need to pick a base point to reference from (usually this is a stationary object that you can measure from. For example, a stationary dock if measuring the tides).
5) Determine the amplitude of the function.
6) Determine the vertical translation of the function.
7) Use the information gathered to create a function of the form , and a function of the form .
8) Graph your functions by hand. (Remember to include appropriate labels, scale, etc.)
9) Using the functions that you have created, determine the yvalue at the point and .
(For example, if your period is 4 , then )
Part 2: Presentation and Reflection
At this point in the course, you have submitted several assignments of various types. For this assignment, you may choose how you would like to present your findings. Please remember that your submission should be appropriate to the course, should be clear and easy to follow, neat and organized. See the rubric for this assignment for further details.
Be sure your submission answers the following questions as well:
1) Describe in your own words why the object or event you chose is periodic.
2) Explain your process for coming up with the functions that represent your object or event. Explain the point of reference you chose and why you chose it, how you measured or gathered the data you need, etc.
3) Explain a method you could use to verify that your functions are accurate (think about ways you have verified functions before, this may have been done in other units, or other courses).
4) Reflect on the assignment. What part of the assignment did you find most difficult? What did you find the easiest? What did you learn while working through this assignment?