Develop the appropriate dimensionless parameters for the period \(\tau\) of transverse vibration of a turbine rotor of mass \(m\) connected to a shaft of stiffness \(k \doteq F / L\) and length \(\ell \doteq L\). Other relevant dimensional parameters are the eccentricity \(\varepsilon \doteq L\) of the center of mass of the rotor, the speed of rotation \(N \doteq 1 / T\) of the shaft, and the amplitude \(A \doteq L\) of the vibration.