Developed by Kelly Roos  Published July 17, 2016
DOI: 10.1119/PICUP.Exercise.SHHO
Subject Area  Mechanics 

Levels  First Year and Beyond the First Year 
Available Implementations  C/C++, Fortran, Glowscript, IPython/Jupyter Notebook, Mathematica, MATLAB, Python, Spreadsheet, and Easy Java Simulations 
Learning Objectives 
Students who complete this set of exercises will
 be able to build a model of a simple hanging harmonic oscillator using the Euler algorithm (**Exercises 1 and 2**);
 be able to build a model of a simple hanging harmonic oscillator using the EulerCromer algorithm (**Exercises 4 and 5**);
 be able to produce graphs of the positon, velocity, and total energy as a function of time from the results of their computational model (**Exercises 15**);
 be able to assess the accuracy of two different computational algorithms (Euler and EulerCromer) by comparing results from the different algorithms to each other and to the exact analytical solution (**Exercises 15**);
 discover that they bloody well can't use the simple Euler method when modeling an oscillatory system (**Exercises 13**).

These exercises are not tied to a specific programming language. Example implementations are provided under the Code tab, but the Exercises can be implemented in whatever platform you wish to use (e.g., Excel, Python, MATLAB, etc.).
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Credits and Licensing
Kelly Roos, "Simple Hanging Harmonic Oscillator," Published in the PICUP Collection, July 2016, https://doi.org/10.1119/PICUP.Exercise.SHHO.
DOI: 10.1119/PICUP.Exercise.SHHO
The instructor materials are ©2016 Kelly Roos.
The exercises are released under a Creative Commons AttributionNonCommercialShareAlike 4.0 license