I'm not an apple user, but a quick search shows:-
10 Creative Ways to Use the Accelerometer [iPhone]
Look at the last item starting "context logger" - can't be any harm in trying one or more of these apps.
The FFT analyser however is the biggie to get meaningful analysis. Whether any of those packages include such capability, I've no idea but if you have an iTunes account, I'm sure you can find out quickly enough.
My experience is that you are likely to find that the main resonances are at frequencies which are a factor of the engine speed. So, for example if you are running the engine at 2000rpm, which equates to 33Hz, you are likely to get modes at 33, 66, 99, 132Hz, and possibly 16 and 8. It's the magnitudes that are important.
I did some work on this with the Jabiru engine some years back, after an entertaining flight test incident where a CFRP propeller spontaneously combusted. If you PM me an email address I'll see if I can find a copy of the report, but in a nutshell the factors were:
- Tip Mach number (anything above 0.8 became problematic, and vibration was substantially less below 0.7)
- Fuel type: mogas giving a similar pattern, but much larger resonance peaks than 100LL. 91UL wasn't around then, so I can't offer an opinion about that.
- Propeller rotational inertia was also a significant player. The low inertia 2-blade wooden props that for example is standard fit on the Jabiru aircraft provide much smaller resonance peaks than the popular modern high inertia composite props such as the Arplast or Warp Drive (possibly the best brand name ever for a propeller!)