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December 22, 2010
I constructed the simple harmonic motion page for a physics lesson. I had this dynamic image in my mind when I learnt the topic years ago! However, I could only stare at the equations and mentally register the interdependencies of different terms. I suppose that most students would have done the similar mental and manual exercise: plot a few different versions of the oscillation corresponding to different sets of controlling parameters. It was the process of training to be a mathematician or physicist. Now, it is a wonderful experience to see the instantaneous response of the changes graphically.
"The simple harmonic motion with damping" page is not a simulation. Actually, the analytic solution to the second order linear differential equation was entered into the page directly. Geogebra simply plots the graph. The spring was a locus of a point on a small circle rolling up the y-axis! I certainly have done a lot of thinking on the topic of "constructions and loci".
The pages that I created can also be viewed and downloaded from http://sites.google.com/site/huivictorc/geogebra.