Calculus
Activity:
Gettin’ the Swing
Posted on Dec 18, 2008
Topic: Derivatives
In this activity, students will investigate sinusoidal functions, collect data from a swinging pendulum, model the data with a cosine function, and take the derivative to find the velocity and acceleration. Self-check multiple-choice questions help students review and build the foundation for their data collection and mathematical model activity.
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Activity Key Steps:
Students begin the activity by reviewing the range, period, and amplitude of a sinusoidal function using self-check multiple-choice questions.
Students will then explore sinusoidal functions and the effect of the parameters using sliders. They will continue to answer multiple choice questions to solidify their understand of A, B, C, and D in the equation y = Acos(B(x – D)) + C.
Use of a slider, spreadsheet, and a graph on a Data & Statistics page help students conceptually derive the relationship between B and the period.
In Part 2, students connect a motion detector and easily begin collecting data of a swinging pendulum. Student will write a function which models the data and take the derivative to model the velocity and acceleration. Students can verify their solution with the velocity and acceleration data. Additional data is supplied for use as an extension or for students who don’t have access to a motion detector.