There may be as many as four types of vibrations involved, two of which require the length, modululus of elasticity and area of the supporting cable. First is the extensional mode of the concentrated bar mass at the end of the cable
f=(1/2pi)*(k/M)^0.5 where k=EA/L for the cable. Second is the pendulum mode (between the guide boundaries)of the concentrated mass about the cable end pivot point f=(1/2pi)*g/L where L is cable length. Third is the beam bending modes of the rod with end and 2/3*l guided or hinged supports where l is tube length. Tables 8-3a to f in Blevins give equations and parametric data for 6 modes of up to 15 equal spans of pinned supports. Table 12-1 in Blevins gives equations for shell modes of the tube in the unrestrained condition, at best an apprtoximation to a guided tube's shell responses. The total range of "natural frequencies" for these four types of vibration probably range from very low (pendular<10 Hz) to rather high (shell modes>1000 Hz)so criticality of calculation accuracies depends on what kind of damage concerns you.
