You can measure the Fr by bouncing the component up and down on the air tube and timing the cycles per second. But because there are a lot of variables involved, including how the component is mounted on the air tube, how the air tube itself is mounted, where it’s mounted, etc.
Furthermore, an inner tube is not an ideal geometry. An ideal geometry is low surface area on top and large volume. A long vertical tube would be ideal in terms of geometry but would be very difficult to work with because it would be very floppy. My original Nimbus Platform used a single air spring, which is relatively floppy so the design needed a secondary horizontal sprung system to build up lateral support. The Nimbus airspring was fitted with a large auxiliary air canister to provide a high effective internal volume of the airspring.