well i tried a different approach to shaking a can of spray paint. I was trying to eliminate as many moving parts as possible. So I thought that using an electromagnet would shake the can with enough force to mix the paint.

Using the transformer from a microwave oven I cut the laminations at the weld seam and removed the secondary coil and the resonant tank coil (the coil attached to the capacitor) leaving just the primary coil and core. Long story short the can acted as a core and carried the flux thru the can and held the can in place. i introduced a gap to no avail. BUT when i added a permanent magnet to the base of the can the DC bias caused the can to vibrate enough to cause the mixing ball to be heard. It wasn't enough to mix the paint very well I don't think.

the primary coil of these transformers has the core in a saturated condition already so there is no reason to increase the flux density.