Developing an Interactive Computer Program to Enhance Student Learning of Dynamical Systems

Today’s students are quite accustomed to availing themselves of the latest in computer innovations and technology to aid in learning and the attainment of student outcomes. For example, use of tablets and cellphones in the classroom to take notes, collaborate on projects and to search the web for information is commonplace. Likewise, advancements in computer software and tools afford in-depth simulations of both mechanical and thermal systems. MATHEMATICA, with its symbolic and visual capabilities, is one such tool that, despite its robustness, is less utilized in classroom environments and is more integrated as a tool for those who pursue research in every discipline from economics to engineering. In this paper, the capabilities of MATHEMATICA are explored as a tool to model and visualize the forced mechanical response of viscoelastically-damped, multiple degree of freedom systems obtained through a Newtonian approach. Proportional damping facilitates the diagonalization of the resulting Eigen-value problem using a Cholesky Decomposition approach. In addition, multiple harmonics can be included as part of the forcing function. Displacement results for each mass permit the generation of graphical results and also provide the needed inputs for animated motions of all included masses. While the ultimate goal is to solve the dynamic response of general nth degree of freedom systems, explicit results are presented for the second, fourth, and tenth order degree of freedom systems to demonstrate the versatility of the software. The program utilized an interactive and user friendly interface developed in MATHEMATICA.