why did my record player slow down, speed up, then go back to normal?

There are also apps on line that provide for your cell smart phone to do this same check.

It is interesting.

Apps such  as RPM, Rotor or true note.

enjoy,

Power surge, or bad belt.

Tenet? 

Happened to me with my older Luxman PD-277.  There are speed control potentiometers for 45 and 33 RPM and they were showing their age.  A little DeOxit cleaned them up.  The wiper contact was a little dirty.

atmosphere is correct. The speed potentiometer might be corroded. This happens a lot on old technics 1200 tt. It's also could be the speed control module.