Vibration on an electric toothbrush

3D layer? Rotation animation? Position animation? There are about a zillion ways to illustrate a toothbrush and at least 3 different kinds of motion. We can't offer much of a meaningful solution unless we know your workflow. Here's a 2D approximation of a Sonicare created with two shape layers, the top one 2D, the bottom one 3D with two X rotation keyframes plus and minus 20º that are one frame apart with a loopOut("pingpong") expression. The top 2D copy has the Transform Bristles opacity set to 60% and the Comp motion blur is set to 200º and -90º for  Shutter Angle and Shutter Phase. The screenshot gives you everything you need to recreate the project except the shape of the paths.

Here's a Sonicare Toothbrush project for you to look at. Took me about 10 minutes.

If at all, a sinus/ cosinus expression would be appropriate, but even that may not get you the "correct" result with the actual point being that the frequency of the vibrtation is way too high to be captured in such detail at normal video framerates and in turn this means that any expression running at such high frequencies would also produce sampling artifacts/ stuttering that look unrealistic. All that being the case, you'll probably have better luck to simply use distortion effects to simulate the extensive motion blur/ smudging.

Mylenium