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Mr. P.: Good morning! Previously we showed that circular motion, when viewed from the side, is simple harmonic motion. Now we are going to derive a position equation for an object in simple harmonic motion. ♫ Flipping Physics ♫ Mr. P.: Lets look specifically at the location of a dot which is motion tracked to the top of the yellow marker cap. And lets pause the demonstration. We can find a relationship between several variables. First, we need to define them. r is the radius of the circular motion, x is the position of the cap in the x direction, assuming the center of the turntable is the center of our coordinate system, and theta is the angular displacement of the cap from an initial position where the cap was at its extreme position to the right. Cosine theta equals adjacent over hypotenuse, or the x position divided by radius. Multiplying the equation by radius gives us the x position of the cap equals radius times cosine theta. Our goal is to determine the position of the cap
