heh.... I was wondering this lately... sitting around on campus watching girls walking by... it seems that there's a natural frequency for, er, bouncing
when they're walking at *exactly* the right speed (usually walking pretty fast but still short of running/jogging), there can be some extreme bouncing going on. Of course it would vary from girl to girl, depending on certain characteristics...
but to the topic, what exactly are you talking about measuring? I would just wait until it hits the resonant frequency (indicated by much greater amplitude -- you should be able to tell by looking at it), and (if feasible) have the oscillating object hit against some switch that starts a timer, or trip a laser beam connected to a sensor. You could estimate the frequency with a simple stopwatch, but for any sort of accuracy you'll need a timer that is set off by some triggering apparatus.
Or wait, are you talking about the *acoustic* resonant frequency of an object? If so, you'd need a device (laser sensor?) that will take very precise measurements of very tiny movements (vibrations). Point it at the object. Get a wide-range, loud sound system.... turn it up and do a frequency sweep from say 10Hz to 1kHz. Plot the amplitude (of the object's vibration) vs. frequency of the sound you're emitting.... any frequency where the amplitude rises suddenly, would indicate a resonance frequency. You possibly could do this without a special sensor, just by touching the object. Things like desks and walls will often vibrate enough to feel them when you hit their resonant frequencies. Most of the time you shouldn't feel it vibrating at all... then when you hit a resonant frequency you should feel it vibrating.
In general I don't know if living items are uniform enough to have a single resonant frequency. Probably your femur has a certain resonant frequency, which is different from that of your skull, which is different from that of your stomach, etc. I know that I get a funny feeling in my stomach sometimes when I'm at the movies or someplace where there's really loud bass at a certain frequency, but usually it's just my stomach and no other part of my body.