• 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

• Animated powerpoint
• Handouts (after lesson) pdf