Modeling the Harmonic Motion of a Mass-Spring System

Spring Movie

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Activity: Modeling the Harmonic Motion of a Mass-Spring System

Objective: To help students visualize rates of change and their properties

This experiment can be used in a general education mathematics class, a calculus class, or a differential equations class when studying periodic functions or harmonic motion. For this experiment, we set up a mass-spring system, put it into motion, and recorded a video of the periodic motion of the mass. After importing the frames of the video into TEMATH, we used TEMATH's Point tool to mark the position of the mass in each frame. The x-coordinate of the positions were placed into a table and plotted as a function of time. The pattern of the plotted points was a sinusoid of the form

y = a sin((2/T) (t-b)) - c

where a is the amplitude, T is the period, b is the horizontal shift, and c is the vertical shift. Using the plotted points and TEMATH's Line tool, students can estimate the four parameters of the sinusoid. The sinusoid can then be plotted on top of the points to determine how well it models the periodic motion of the mass-spring system.

Click the buttons to see the fit

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