A Qualitative Analysis of Simple Harmonic Motion

Simple harmonic motion (henceforth SHM) is taught at various levels depending on students’ maturity in mathematics.¹ Without delving into much mathematics, this paper qualitatively analyzes SHM based on elementary knowledge in kinematics, Newton’s second law, Hooke’s law, and mechanical energy conservation, which students are usually exposed to before the introduction of SHM. The results from the analysis are used to sketch the velocity vs. time curve, and the shape of the curve is largely determined by the fact that the tangent line slope on a velocity vs. time curve is the instantaneous acceleration. Even though the obtained curve is not proven to be sinusoidal here, it visually appears to be. The value of this approach is that key features of the seemingly complicated motion can be revealed to students who are not mathematically well prepared. Moreover, students are exposed to intensive physical reasoning rather than dry mathematical manipulations even...