This thing is inspired by an excellent instructable at
http://www.instructables.com/id/Slow-Dance-a-Fusion-of-Art-and-Magic/?ALLSTEPS
Since not all of us are experienced wood workers, we do without the frame and use some power leds to illuminate the objects from below, like on stage. Since spring steel strips are not always easy to get, some feeler gauges (0,3-0,25 mm) are used as springs. A hole is already present. Small neodymium magnets clamp themselves to the feeler gauges. The distance of the 0,25mm feeler gauge to the magnet is slightly larger to compensate for the higher flexibility. The coil is operated in push pull mode to have maximum amplitude. The frequency of the coil is 80Hz. The blink frequency of the leds is slightly below that frequency. Adjust the LED control to realize optimum effect. The first video shows the operation at a lower frequency.

The length of the coil is 65 mm, the diameter 25mm.With a wire diameter of 0.35 mm this results in a resistance of about 8 Ohms. The steel core has a diameter of 10 mm.
A led setup is demonstrated in one of the photographs. After some time, they get quite hot. If the unit is used for a longer time, it is better to solder the leds at the copper side of a PCB, using heat conductive paste between the leds and the copper. At the back, an additional heat sink can be added. Two o-rings clamp the object.
Since the leds and the coil have to be controlled individually, some complicated programming is required, because the delay() function influences both. That problem is bypassed by using two microprocessors (ATtiny85). Two small sketches and one L293D H-bridge IC complete the set up.
Feel free to design and print a nice housing.