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# Single Simple Harmonic Oscillator

## The Prompt

**“A single particle is allowed to move between two fixed points. The springs both have spring constant** $\kappa$**. 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.

## Wrap Up

On the path to describing an arbitrary one-dimensional chain of atoms, this is one of the simplest cases that can be depicted. For students with less experience in differential equations, the wrap-up of this activity will also demonstrate that the D.E. describing a system is the key to finding the equation(s) of motion for that system.