Animation As The Final Step In The Dynamics Experience

A method of incorporating animation into the student experience in the analysis of dynamics (especially vibrations) problems is presented. After a student models the problem, draws freebody diagrams, and derives equations of motion, he/she then obtains the solution for the position coordinates as functions of time. The student generates and plots the solution within a simple MATLAB program in which all parameters, such as mass, stiffness, damping, lengths, initial conditions, etc. can be easily changed. The solution can be generated using either a closed form solution or a numerical differential equation solver. In either case, at the end of the program, the student can animate his/her own solution by running an animation function file provided by the instructor. The function file requires a simple one-line command to run it. The function file does not solve for the motion of the system; it merely provides the animation graphics. Specifically, it displays the system in motion in real time (according to the student’s solution) while simultaneously redrawing the student’s plots. The animation function files are problemspecific. Several have been created by the author and are available for download. The advantages of this approach to animation are that: i) it is simple, requiring only an elementary knowledge of MATLAB, and no additional software, ii) it can be used with either closed-form or numerical solutions to the problem, iii) it provides a physical interpretation of a student’s mathematical solution (even if his/her solution is wrong!), and iv) it easily facilitates the investigation of how the parameters of the problem affect the motion. Four examples will be presented to illustrate the scope of this method: i) a basic free spring/mass/damper, ii) a multi-degree of freedom system, iii) a suspension system subject to shock (requiring numerical solution), and iv) a dynamics problem (the rolling/slipping wheel). The author’s overall goal in using this approach is to provide students with a cumulative experience in dynamics, understanding how the complicated motion of systems results from the basic laws of mechanics. This method of using animations has been used in the author’s vibration course. Some feedback from the students on its effectiveness will be presented. Finally, there will be a short section describing the basic techniques used by the author to program the animation files