In deep drilling applications, high-frequency torsional oscillations (HFTO) ranging from 50 to 500 Hz occur as a result of the interaction between bit and rock with velocity-weakening characteristics of the torque on bit. These self-excited torsional vibrations impair drilling efficiency and may lead to tool damages. Consequently, the reduction of these vibrations is pursued. One possibility to reduce HFTO is the application of torsional dampers in drill strings. To optimize the design and positioning of the dampers, an appropriate model of the drill string with dampers in the event of self-excited vibrations is necessary for better predictions of HFTO frequencies and loadings. However, the damper parameters exhibit nonlinear dependencies on both frequency and amplitude, which poses a challenge to the modeling of the damper. To address this issue, a theoretical investigation is carried out on a minimal model as a preliminary step to characterize these nonlinearities and the resulting effects. This involves firstly comparing the results of the frequency response function with those of linear modeling methods, such as modal analysis. The frequency response analysis enables the frequency dependency to be described effectively without iterative calculations, in contrast to the modal analysis. Additionally, it is discussed to which extend this approach that is usually used for externally excited systems can be transferred to self-excited systems. To answer the question of the necessity of considering amplitude dependencies, a parameter sensitivity analysis is also performed to investigate and estimate its influences. The results of these investigations can be applied to a realistic drill string system and contribute to optimizing HFTO mitigation performance by torsional dampers.