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Wednesday, March 24, 2010

How to find solutions for simple harmonic motion (SHM)

Simple harmonic motion is a subset of periodic motion, defined as motion that depends on displacement. Springs certainly follow this definition since Hooke's law gives us F = -kx. This picture of a mass oscillating at the end of a spring also makes use of energy, U = .5kx^2. But our goal is to understand the motion as a function of time, as well as a function of position. Bringing time into the picture is the issue, and it turns out we need a second order differential equation. This video outlines how to get a solution for position of the mass on a spring as functions of time. Turns out these require sine or cosine functions. Other videos will focus on other details and specific problems to show a general solution we can use.

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