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Intro to Trigonometry and Resonance

Summary

This lesson introduces students to trigonometry through an examination of the simple harmonic motion of a weight suspended by a spring. 
  • We begin by introducing the spring, weight, and the relationship between spring constant, position, force, and acceleration.  Objective is build intuition regarding proportinality and sign - and not for students to memorize equations.
  • Students are introduced to resonator simulation program, predict output, run program, and discuss output.  Concepts periodicity, period, frequency. 
  • Examination of context: by switching initial position & velocity, phase is shifted90 degrees and plots become sine & cosine.   
  • Examination of the relationship between velocity & position by plotting sine/cosine (plot configurations rather than time)..
    • Phase relationships, motivates polar interpretation
  • Introduction of sine & cosine; relate to right triangles with unit hypotenuse. 

Slides

© 2011 Eric Freudenthal and collaborators.  All rights reserved.
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Eric Freudenthal,
Apr 3, 2011, 1:26 PM
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Eric Freudenthal,
Apr 3, 2011, 1:11 PM
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