Mapping circular motion onto linear SHM

 

Yesterday's toy reminded me of this experiment I used to do. I stuck a table tennis ball onto a turntable and projected the shadow onto the screen. As the turntable rotates, the shadow appears to perform SHM.

Unfortunately the letter labels on the schematic diagram below don't correspond to the photo above

But notice that a 90 degree rotation takes the shadow from the middle to the edge so the middle and the amplitude of the SHM have a phase difference of 90 degrees.