Accelerometers built in to modern mobile devices have remarkably good precision and sensitivity. Many researchers have used them to identify natural frequencies of large structures, small mechanical devices, and more.
I measured the natural frequency of a steel cantilever beam by placing my phone at the supported end of the cantilever running the Vibration Analysis app. You can see the 2.79 Hz peak of the fundamental mode of vibration of the beam along with other peaks associated with other modal frequencies.
All apps described on this site are available from the Apple AppStore. Some of them are also availalbe for Android.
Vibration Analysis has the most robust tools for applying windows, adjusting parameters, and visualizing results in real time. You can adjust stop levels and duration, select the accelerometer axis of interest, adjust the FFT size, select units of measurement, and display a list of dominant frequencies. You can also record and export collected data.
Vibration Pro and Vibration apps are set up to conduct highly controlled experiments. You can adjust triggering levels and duration of data collection. The frequency spectrum is available once data collection is complete and allows you to identify the first five peaks. Time series data can be exported.
PhyPhox has a consistent format for all of the "experiments" available to conduct with the phone. "Acceleration Spectrum" is the most useful for vibration studies. You can set the number of samples to be used in the FFT, but it also has a useful History page that produces a waterfall plot of frequency versus time and peak frequency versus time. The "Spring" experiment can be used to identify resonance frequencies using an autocorrelation function. As with all experiments in PhyPhox, the raw data can be exported or points can be viewed within the app.
A very effective mobile acceleration sensing platform can be built using products available from PCB, Apple, and the App Store. Connection is made from the accelerometer to the signal conditioner to the iPhone lightning port. Calibration factors can be applied and data collected using a variety of apps, but the best I have found with specific support for the PCB system is Vibration Pro.
The PCB Digital ICP Signal Conditioner is a 2-channel signal conditioner that works with ICP accelerometers.
PCB has a range of accelerometers available. I use the PCB 333B50 with 1 V/g and the extremely sensitive PCB 626A04 with 10 V/g.
A USB to Lightning Port Adapter connects the PCB signal conditioner to the iPhone.
The Vibration Pro app allows for 2-channel synchronized data collection, frequency spectrum, and peak picking.
Single channel data collection and analysis is available with the Vibration Analysis app.