A combined translational and rotational system with different combinations of elements is used to find time-domain solutions and observe the forced response of a mechanical system with two degrees of freedom. Mathematical models for all four proposed cases are derived, and the proper outputs are plotted with the aid of MATLAB® and its numerical simulation tool Simulink®. The obtained results in graphs representing translational and rotational movements are analyzed and compared to study the dynamic behavior of the combined mechanical system. The results indicate oscillatory motions for all cases. The influence of removing some elements, like springs and damper, is also investigated. The systems are also modeled in the complex domain, and the proper transfer functions are created. Zeroes and poles of these functions are determined, and the stability of the systems is examined through Bode plots and Nyquist diagrams. The results indicate that all observed systems will remain stable after closing the feedback loops, even in cases of increased gains.