I think that the frequency of the system is the one being amplified by resonance.

It depends only on the rod's dimensions.

Your description is not adequate for detailed analysis, but the information you supply is useful for further consideration, as explained below.

The phrase "...motor... on a floor supported by a single rod" is suggestive of some kind of pendulum where the 'single rod' is the pendulum arm, and the motor is the 'bob' of the pendulum. For a simple pendulum, natural frequency is nonlinear with amplitude that may be treated approximately as linearization for small angle displacement of the pendulum arm by assuming sin(theta) approximately equals theta where theta is the angle of deflection of the pendulum arm. Simple pendulum frequency is primarily inversely dependent on arm length, given all other parameters the same.

You also imply that the 'rpm frequency' is different from the 'whole system' frequency. This seems to be a situation where the motor on the arm is a pendulum with one frequency but the voltage-dependent motor rpm is an independent response from the pendulum. The two effects will appear to be independent when the motor 'frequency' is of a different order than the pendulum frequency (probably much higher than that of the pendulum), or while the motor rpm is constant as you indicate. In this case, if you were to put a gear reduction on the motor to bring its output rpm into proximity with the pendulum frequency, then the two motions may interact much more. This could be further investigated by attaching an inertial load like a disc or bar on the reduced-rpm output shaft to couple substantial inertia to the motor, increasing its inertia to be similar to that of the pendulum supporting the motor.

Remember that rotational inertia, the important quantity for both pendulum and motor systems, varies with the square of distance from rotation axis to the mass of the object. This radius of rotational inertia is also known as the radius of gyration. Further, rotational inertia must be treated carefully. Any object will have one rotational inertia value for rotation about its own center of mass (CM), but an additional term is required if the center of rotation is offset from that center of mass. This additional term is derived by the parallel axis theorem, and is essentially equal to m times r squared, where m is the mass of the object and r is the radius of the CM from the rotation axis.

If you can get the rotational inertia of the motor-&-disc system to a similar order as that of the pendulum system, then you should see some effect expressed in the pendulum frequency when varying the motor rpm . This will likely only happen as you are changing the motor rpm (i.e. changing the motor control voltage), since a constant motor rpm will produce minimal or no torque reaction on the motor support.

An important tip for this type of analysis or consideration is to start at the basics - make a free body diagram (FBD) for the pendulum system, and another for the motor and anything attached to its shaft. The reaction forces of the motor support my then be expressed as term(s) in the pendulum FBD equations to define the coupling between the two systems. Writing these bases of governing equations this way using carefully contemplated FBD expansion should immediately make it clear that the correct amount of motor shaft inertia will indeed influence the behavior of the pendulum, i.e. its fundamental frequency.

Irrespective of the contexts, the frequency of a signal remains constant in non-dispersive media