This can be done relatively easily, depending on the type of analyser that you have. You have to be able to store a series of spectra obtained at known time intervals and present them in a '3-D' or waterfall format.
Keeping the machine at steady operating conditions, take 5 spectra (no-averages) at say 2 second intervals - then start impacting: begin with light taps using a hard rubber/plastic mallet at 5 taps/second) and take another 10 spectra also at 2 second intervals, followed by another 5 spectra also taken at 2 second intervals with no impacting.
Plot the specta in a waterfall format and you can see the effects of any excitation of a natural frequency (unless it is always visible due to being excited during during normal operation). There's a bit of trial and error involved, but once you can see that you are getting results, you can fine tune the procedure.
I have carried out this test with Adre and Zonic book systems, both of which allow you to automatically schedule spectrum capture at fixed time intervals. With a bit of thought and planning you could also do this with a hand-held datcollector system.
Of course, this will only tell you if there is a natural frequency present close to your measurement point and not its location (foundation/bearing housing/casing/shaft or piping).
A better way of identifying natural frequencies associated with rotating equipment is to measure 1X (and nX) amplitude and phase during a shutdown (or slow startup) and inspect the bode and polar plots - for that you would definitely need an Adre or Zonic book and fit the machine with a keyphasor (once per rev tacho/reference pulse)