Simple Harmonic Motion - Teaching Methods in First Year Engineering Course (July 2021)

The importance of First Year Engineering Student (FYES) retention and overall success is predicated on their recent academic success in high school. Too often a struggling first semester student has limited knowledge of how a mathematical equation relates to a physical concept, for example, the mass-spring system as in Simple Harmonic Motion (SHM).A freshman engineering student typically takes Algebra/trigonometry, Pre-Calculus or Calculus where functions are presented. The purpose of this paper is to describe the teaching method used for explaining SHM using the sine wave function, MATLAB and everyday-life analogies along with lessons learned. Through practical lecture material of wave motion and hands-on problem solving using MATLAB, the freshmen student learning is enhanced. Survey results from the freshmen engineering course are compared against upperclassmen with race/ethnicity factors in two mathematics courses.Freshmen students were surveyed on their understanding of the meaning of a sine wave function and sound wave as it relates to MATLAB programming, for example, a vector of sine waves of varying frequencies. Then the sine wave motion was conceptualized to one-dimensional motion in terms of a mass-spring system and the equation for displacement and velocity.Course modules were taught in the Problem Solving for Engineers course for freshman and Differential Equations for upperclassmen in Fall of 2020. The Problem Solving for Engineers course teaches students how to apply mathematics to the real-world including problems encountered in everyday life and while taking freshman engineering courses. Each course module has two parts: a) three virtual lecture classes with PowerPoint presentation on trigonometry, wave motion and MATLAB coding and b) a hands-on lab exercise using basic MATLAB commands to simulate wave motion. The upperclassmen lecture was taught face-to-face by the co-author mathematics professor.One-hundred and two (102) students were used for the learning study of sine-wave and SHM. Freshmen learning outcomes, such as interpretation of the displacement equation, are compared to upperclassmen. Freshmen students in both the Problem Solving for Engineers and Pre-Calculus for Engineers and Scientists, as well as upperclassmen in Differential Equations I , were also surveyed on their understanding on simple harmonic motion and related equations.A pre-survey has been completed and a post-survey will be conducted anonymously before and after the teaching modules. Preliminary results indicate that 'hands-on' exercises are necessary to increase the learning effectiveness of freshmen and understanding of SHM. A quantile plot comparison of students’ self-rankings before and after the two modules for each of five learning objectives will be presented.Future work this year in FYES teaching is practical demonstrations on the relationship between the physics of a sporting event and motion. The semester culminates in the student's hands-on exercise. The survey results will also be used in the Differential Equations course to better understand effects of active learning on students’ perception of mathematics through their engagement, satisfaction, and perceived performance in the class.Dr. Horne has begun a work-in-process of studying " Teaching Methods in Engineering Problem Solving Course". The purpose of this work is to describe the teaching method used for explaining wave motion using MATLAB and lessons learned. One such classroom experiment utilizes sound waves of varying frequencies generated by a piano tuning fork. The fork is then positioned close to a microphone/speaker connected by a electrical conductors/wires to an oscilloscope. The sound wave energy is transferred to an electrical wave. Furthermore, students are assigned a project to complete a song of three different frequencies using the MATLAB programming language. As Dr. Horne says " The student seeing the sound wave transferred to an electrical wave and then writing the sine function on the board is 'mathematics in action'. Through practical lecture material and hands-on problem solving using MATLAB, rather than pure theoretical mathematics, the freshman student learning is expected to be enhanced.