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Simple Harmonic Motion

Activity Overview

Students explore simple harmonic motion in terms of the motion on a swing. Students derive the defining formulas - first, beginning with the trigonometric relationship between time and displacement, and differentiation to the form for acceleration, and then by integration from acceleration back to displacement.

Key Steps

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    Students graph a given displacement equation for the swing.

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    They can graph the equations for y2 and y3 by finding the derivative by hand. After each graph, students should answer the questions on the worksheet.

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    Students can closer examine rates of change of displacement leading to velocity, and rate of change of velocity leading to acceleration. By building an understanding of the concept of acceleration, they form the basis for deriving the forms for simple harmonic motion.

    Students will see that substituting back leads to the defining equation in terms of acceleration and displacement.