It is well known that adjacent structures may collide with each other during severe earthquake leading to pounding force, and as a result, damage and even destruction can be observed in these structures. Implementing or connecting structures with energy dissipaton elements is one of the ways to avoid collisions. In this study, the seismic behavior of a single degree of freedom (TSD) system pounding to a rigid wall was investigated and the viscous damper capacity to prevent the collision was determined by optimization study. The displacement responses of the structure under the earthquake load is required to be limited in order to prevent the occurrence of pounding forces. By analyzing the seismic responses for various gap values, the frequency-time relationship of the displacement responses observed in the absence and presence of collisions were investigated by continuous wavelet transform. Thus, the differences in the frequency content of the displacement signal for variable gap values were determined. In addition to these, the minimum linear viscous damper (LVD) capacity, which vanishes the pounding force was also investigated by the optimization study. In this study, wavelet coherence analyzes of displacement time series were performed as a first. Coefficients of coherence between the collision-free state and the collision-induced displacement responses for various gap values were obtained. The additional damping ratios were increased gradually until the pounding force became zero. The damping ratio, was determined as the additional damping ratio that should be added to the structure when wavelet coherences converged to 1, and the damper capacity was calculated. When the LVD damping coefficient obtained by the optimization study was added to the system, it was observed that the pounding does not occur.