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.
© 2011 Eric Freudenthal and collaborators. All rights reserved.