dna - There are linear and rotary molecular motors in the cells. Do any of them have a fixed or stable frequency or speed?

These molecular motors' response maybe dynamic and nonlinear. But it entirely dependent on the external influence and also the characteristics of the motor itself including number of active motors involved in operation. As it is microscopic, it will not possible to analyse by assumptions and say they have some random frequency. They do have certain frequency of operation (I do not know whether they are controlled by biological clock or some master clock but they are controlled by nucleus of the cell) and "Modeling molecular motors" explains how motors act on the filament inside the cell. It mainly talks about the influence of external force on the operation of motor and also speed(v) of the motor. The following excerpt from that paper talks about the external force on motor.

The action of the motor is induced by generalized forces, which for
the motor/filament system may be identified as the mechanical force
fext applied to the motor, and the chemical potential difference
Dm, which measures the free-energy change per consumed ‘‘fuel’’
molecule. The force fext describes external forces, for example of
optical tweezers, microneedles, or the viscous load of an object that
is carried. fext could also include viscous friction forces between
the motor and the surrounding solvent if the latter is considered as
‘‘external.’’ The chemical potential difference Dm is for the
process of the hydrolysis of Adenosinetriphosphate (ATP) to
Adenosinediphosphate(ADP) and phosphate (P).

The frequency of molecular motor according to "Biophysics of Molecular Motor" has been classified into two categories:

1. Density controlled: In the density-controlled model, it is assumed that the depolymerization rate is proportional to the motor density at the terminal site of the microtubule. Here the frequency of motor is dependent on density of the motor.




2. Flux controlled: Filament depolymerization is determined by the flux of motors
   to the end. Here the frequency is dependent on the flux of the motor.

In both the above cases the length of the filament on which motor is acting is also important. These models have been analysed and plotted on a graph to give a clear picture of it.

The paper explains the catastrophe frequency, the frequency at which the filament shrinks. Shrinking of of a filament is due to motor. So the paper concludes saying the catastrophe frequency is 0.5 per min for a 8um length of filament.

(Catastrophe = the transition from growing to shrinking of dynamic microtubules).

To summarize, these motors do have speed and frequency of operation but they are not fixed. They vary in a non linear fashion due dynamic environment. But the motor tries to be as much stable and resistant as possible.