A Qualitative Analysis of Simple Harmonic Motion.

This article provides a qualitative analysis of simple harmonic motion (SHM) using elementary knowledge in kinematics, Newton's second law, Hooke's law, and mechanical energy conservation. The analysis focuses on sketching the velocity vs. time curve, which is largely determined by the fact that the tangent line slope on this curve is the instantaneous acceleration. While the obtained curve is not proven to be sinusoidal, it visually appears to be. The qualitative approach complements rigorous mathematical approaches and provides rich physics content. The article also discusses the preparation and details of curve sketching for the velocity vs. time curve. Overall, this qualitative approach can be used to introduce SHM to students and help them understand the motion without relying on complex mathematics. [Extracted from the article]