To obtain the equation of motion fo

To obtain the equation of motion for the undamped free
torsional vibration of the system, the damping and the excitation torque are set to zero, i.e., C = 0 and t = 0. The resulting
system of equations corresponds to an eigenvalue problem,
which can be solved easily to give the natural frequencies and
mode-shapes of the system. The first four natural frequencies
are tabulated in Table 2, and the corresponding mode-shapes
are shown in Fig. 2. Note that they are plotted using a logarithmic scale as the relative amplitudes between various positions can be very large. Note also, that as the modulus of the
mode-shapes is plotted, the positive and negative angular
displacements are indicated by different line-styles.