The MicroSet Precision Clock and Watch Timer can be used to vibrate hairsprings.This image shows the basic setup. The hairspring is held in a tiny flat-jawed alligator clip which has been ground to a fine, tweezer-like tip. This tiny clip is held in a larger alligator clip. This clip is supported by a "third hand" to allow adjustments to the height of the spring.
The hairspring and balance are suspended over a small section of clear acrylic plastic on rubber feet. With the alligator clips slightly raised, the spring is slightly extended, and the balance wheel pivots on the surface of the plastic.
A special optical detector is slipped underneath the plastic platform and faces upwards.
Overhead (out of view) is a 60 watt lamp, covered with tin foil. A hole about the size of your finger has been punched through the foil. This provides a relatively collimated source of light which shines on the whole assembly. The balance wheel casts a distinct shadow on the detector and the white paper underneath it.
To take a reading, the balance wheel is carefully twisted by hand and set in motion. It will continue to oscillate pretty reliably for about a minute and a half. As it oscillates, the shadow of one arm passes over the detector, which triggers the MicroSet timer, which I have set up to record the rate of oscillation on a laptop computer.
Shown below is a MicroSet graph of three separate runs of the setup. As you can see, the readings are quite stable. In this setup, the spring is clamped in the wrong place and the rate is too slow (the correct rate is 18000 BPH). Within each run, the fluctuation in rate extends about half the distance between two grid lines. Since the graph is labeled (in the lower left corner) "Each grid line = 1.6 mins/day", the variation in rate of the freewheeling balance is within about 0.8 minutes per day.
This hairspring setup is available as a MicroSet Accessory. It includes the special detector, a small plastic platform, and a tiny smooth jawed clip to hold the spring. You will need to acquire your own "3rd hand" to hold the small clip. These can be purchased at Radio Shack.