In this article, for the necessity of measuring the damping of new materials, a detailed comparison was made between two important free vibration torsion pendulums, that is, the inverted torsion pendulum and the Collette pendulum. Special attention was paid to the strong effect of the torsionally weak suspension in both pendulums on the difference between measured damping of the overall system and the real damping exclusively contributed by the investigated specimen. This difference was successfully quantitatively characterized by a parameter: the sensitivity of the pendulum only via which the accurate damping for the specimen can be determined for each case. The comparison showed that the sensitivities of the two systems obviously behave differently. Although it produces smaller performing strain amplitude on the specimen and has a narrower preset vibration frequency range, the sensitivity of the Collette pendulum is always lower than that of the inverted torsion pendulum. ©1996 American Institute of Physics.