A Qualitative Analysis to Simple Harmonic Motion

TL;DR

This paper presents a qualitative, physics-based approach to understanding simple harmonic motion, aiding students with limited mathematical background by focusing on velocity and acceleration variations.

Contribution

It introduces a visual, conceptual method for analyzing simple harmonic motion that complements traditional mathematical techniques.

Findings

Velocity-time curve appears sinusoidal

Approach helps students grasp physical reasoning behind SHM

Complementary to rigorous mathematical analysis

Abstract

This paper proposes a qualitative analysis to the simple harmonic motion for students who are not mathematically well-prepared. It uses the variation in speed and acceleration to sketch the velocity-time curve. The curve appears to be sinusoidal, whose shape is largely determined by the fact that the gradient of a velocity-time graph is acceleration. This approach cannot determine the exact value of period and claim the curve to be sinusoidal, however, it complements rigorous mathematical analysis in that it is full of physical reasoning that the mathematical approaches lack of.