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# Single Simple Harmonic Oscillator

## Prompt

** “Consider a single particle that is free to move between and connected to two fixed points on opposite sides by springs with spring constant **$\kappa$**. The system is one dimensional. What is the differential equation that tells this atom what to do?” **

## Context

This SWBQ will help gauge how familiar students are with describing classical harmonic oscillators (particularly through use of Hooke's Law) in terms of differential equations. For students with less experience in differential equations, the wrap-up of this SWBQ will also demonstrate that the D.E. describing a system is the key to finding the equation(s) of motion for that system. On the path to describing an arbitrary one-dimensional chain of atoms, this is one of the simplest cases that can be depicted.