Prosthetics play broadly a significant role to enhance mobility and independence for disabilities people. These mechanical devices are utilized to provide functional movements of a human arm in diverse applications such as rehabilitation, sports, and innovation. Therefore, it becomes essential important to assess the dynamic response of human prosthetics. This study focuses on studying the dynamic response of a five-degree-of-freedom prosthetic human arm. The human system was modeled by using Lagrange-Euler method to obtain a five-second-order ordinary differential equations. Then it was linearized to facilitate the optimization process required to gain local optimal system parameters. A comparative analysis was then conducted between the linear and nonlinear systems responses to ensure that the linearized system can successfully able to compensate for the real system. The arm parameters (masses, damper coefficients, and stiffness) were selected relying on a Lagrangian multipliers method while achieving short settling time and low overshoot Eventually, the system performance of the proposed system was investigated while involving a wide range of initial excitations. The results showed that all parts of the human arm (elbow, forearm, and hand) oscillated, providing well-suited responses with a short settling time and low overshoot, despite varying initial conditions.