I have an oscilating fan that I would like to vary the fan spin rate. I am doing a color experiment for my physics class to show them that the lights are blinking at 60hz so I need to be able to vary the speed of the fan. Its an old fan that I can take apart. What do I do?

You can try a fan dimmer, they are designed for motors. Just wire a handi box with 120 VAC in , go through the dimmer and an outlet on the other side.