Recent developments in engineered timber products, and their availability, durability, and renewability, have led to taller and more flexible buildings. However, these buildings may experience excessive vibrations, resulting in safety and serviceability issues due to wind or earthquake loads. This paper presents a dynamic analysis of a 42-story-tall hybrid-timber building, along with a comparative study of the performance of three damping devices: (i) pendulum pounding tuned mass damper (PTMD), (ii) tuned mass damper inerter (TMDI), and (iii) tuned mass damper (TMD). First, we evaluate the vibration reduction capability of the TMD and the TMDI under filtered white noise and variable frequency sinusoidal excitations. Then, we propose a robust pendulum PTMD designed using the Hertz contact law to minimize the responses under seismic excitations. For a fair comparison, the mass of the TMD, TMDI, and pendulum PTMD is kept the same. The results show that the pendulum PTMD has higher performance and can reduce the peak accelerations under earthquake loads when both TMD and TMDI fail to achieve this requirement. The superior performance of the proposed device in reducing peak accelerations relates to the reduction in damage to structural and nonstructural components under seismic loads. Nevertheless, coupling the inerter and TMD to form a TMDI may shift the optimum frequency and damping ratios, leading to reduced performance. Compared to TMD and TMDI, the proposed pendulum PTMD is more robust, with higher performance in reducing the base shear (55.7%), base moment (41%), and inter-story drift ratio (40%). The dominant capabilities of this novel device in a timber-hybrid building under different excitations reveal benefits that can shape the future of the physical infrastructure and contribute to climate change adaptation and mitigation for improved disaster resilience and circular economy policies.