An undergraduate study of harmonic and parametric motion of a simple spring-mass system from motion waveforms

TL;DR

This paper presents an undergraduate laboratory exercise analyzing complex harmonic and parametric motions in a spring-mass system, emphasizing waveform analysis and experimental design to enhance physics understanding.

Contribution

It introduces a flexible experimental approach for students to explore complex oscillations and deviations from simple harmonic motion in spring-mass systems.

Findings

Observation of various oscillation patterns

Analysis of deviations from simple harmonic motion

Investigation of parametric oscillations

Abstract

The spring-mass system studied in undergraduate physics laboratories may show complex dynamics due to the simultaneous action of gravitational, elastic, and torsional forces, in addition to air friction. In this paper, we describe a laboratory exercise that caters to beginning students while giving those with more background an opportunity to explore more complex aspects of the motion. If students are not given predefined apparatus but are allowed to design the experiment setup, they may also learn something about physics thinking and experimental procedure. Using results thus produced, we describe a variety of spring-mass oscillation patterns, discussing the physics of the significant deviations from simple harmonic motion. The parametric oscillation behavior we have observed is reported and investigated. This study is based on analysis of motion waveforms.