## A Eureka MomentMay 1st, 2009 Patrick Stein

I was pondering the Phony Physics again as I set to work on my iPhone app.

In the previous post, I twiddled the equations for damped spring motion until I found something visually pleasing. Last night, I went back to the drawing (a.k.a. white) board.

What if I used an exponential spiral (parameterized by arc length). Then, I could easily adjust the number of times it bounces back and forth. I could use a spiral like $r(t) = \alpha K (1-t)^n$ and $\theta(t) = K(1-t)$ where $K$ is some multiple of $2\pi$. Then, I could walk along the spiral getting to the origin when $t = 1$ going around the origin $\frac{K}{2\pi}$ times in the process. If I follow the curve at a fixed rate, then I guarantee that my oscillations will pick up speed as I approach the origin.

Rather than have it spiral into the center, I am just using the x-coordinate of the spiral as my new $t$ value to interpolate with. I like the effect for the most part. It overshoots a little bit far on the first oscillation. I may tweak it some more before it’s all over. For now though, I am sticking with it.

I will post some graphs soon.