Overview and Authoring Guidelines

## The PICUP Collection of Exercise Sets

The fundamental unit of the PICUP collection of educational materials is the "Exercise Set". All Exercise Sets are peer-reviewed and adaptable for faculty use. Standard Exercise Sets use numerical approaches that can be adapted to multiple platforms and Specialized Exercise Sets take advantage of particular computational platforms.

Exercise Type Any
Course Level Any
Subject Any
Programming Language Any
more

## 83 Exercise Sets

### A Rigid Three-bar Pendulum

Beyond the First Year Mechanics

Developed by Ernest Behringer

Example Implementation: Python

### Binary Stars with Equivalent One Body Problem

Beyond the First Year Mechanics

Developed by Aaron Titus

Example Implementation: IPython/Jupyter Notebook

### Center of Mass for Point Particles

First Year Mechanics

Developed by Deva O'Neil

### Computing the 1-D Motion of a V2 Rocket

First Year and Beyond the First Year Mechanics

Developed by David Marasco

Example Implementations: Spreadsheet, Glowscript, and MATLAB

### Double Pendulum

Developed by Derrick Hylton

Example Implementation: IPython/Jupyter Notebook

### Energy and Phase Space of a Damped Oscillator

Beyond the First Year Mechanics

Developed by Deva O'Neil

Example Implementations: Glowscript, IPython/Jupyter Notebook, and Mathematica

### Falling Sphere with Air Resistance Proportional to $v^2$

First Year and Beyond the First Year Mechanics

Developed by Kelly Roos

Example Implementations: C/C++, Fortran, Glowscript, Haskell, IPython/Jupyter Notebook, Mathematica, MATLAB, Python, and Spreadsheet

### Falling through a non-uniform Earth

First Year Mechanics

Developed by Karl Henrik Fredly and Tor Ole Odden

Example Implementation: IPython/Jupyter Notebook

### Foucault Pendulum

Beyond the First Year Mechanics

Developed by Andy Rundquist

Example Implementation: Mathematica

### Harmonic and Anharmonic Oscillations of a Boat

First Year and Beyond the First Year Mechanics

Developed by Eric Ayars

Example Implementations: Python, Easy Java Simulations, IPython/Jupyter Notebook, and Mathematica

### How far would a skydiver have to fall to break the sound barrier in a non-uniform atmosphere?

First Year Mechanics

Developed by Karl Henrik Fredly and Tor Ole Odden

Example Implementation: IPython/Jupyter Notebook

### Lagrangian dynamics

Beyond the First Year and Advanced Mechanics

Developed by Andy Rundquist

Example Implementation: Mathematica

### Making Animations with Potential Energy

First Year and Beyond the First Year Mechanics

Developed by W. Brian Lane

Specialized Programming Language: Glowscript

### Physical Pendulum without Small Angle Approximation

First Year and Beyond the First Year Mechanics

Developed by Gautam Vemuri and Andy Gavrin

Specialized Programming Language: MATLAB

### Plane Rigid Pendulum

First Year and Beyond the First Year Mechanics

Developed by Kelly Roos

Example Implementations: C/C++, Easy Java Simulations, Fortran, IPython/Jupyter Notebook, Mathematica, MATLAB, Python, and Spreadsheet

### Planetoids with Momentum!

High School and First Year Mechanics

Developed by Christopher Orban

Example Implementation: Javascript

### Planetoids with Torque!

High School and First Year Mechanics

Developed by Christopher Orban

Specialized Programming Language: Javascript

### Simple Hanging Harmonic Oscillator

First Year and Beyond the First Year Mechanics

Developed by Kelly Roos

Example Implementations: C/C++, Easy Java Simulations, Fortran, Glowscript, IPython/Jupyter Notebook, Mathematica, MATLAB, Python, and Spreadsheet

### Snowboard Jumping and Newton’s Second Law

First Year Mechanics

Developed by Michael (Mick) O'Shea

Example Implementations: Python, IPython/Jupyter Notebook, and VPython

### Space Elevator - Analyzing Stress

First Year and Beyond the First Year Mechanics

Developed by Larry Engelhardt

Example Implementations: IPython/Jupyter Notebook, Python, and Spreadsheet

### Traveling to Mars

First Year and Beyond the First Year Mechanics

Developed by Aaron Titus

Example Implementations: Glowscript and Easy Java Simulations

### Calculating the magnetic field with the Biot-Savart Law

Beyond the First Year Electricity & Magnetism

Developed by Jordan McDonnell

Example Implementations: IPython/Jupyter Notebook and Fortran

### Charges in a conductor and Gauss's Law

First Year and Beyond the First Year Electricity & Magnetism

Developed by Larry Engelhardt

Example Implementations: C/C++, Easy Java Simulations, Fortran, Glowscript, IPython/Jupyter Notebook, Mathematica, and MATLAB

### Chargesweeper (similar to Minesweeper)

First Year Electricity & Magnetism

Developed by Deva O'Neil

Example Implementation: Glowscript

### Charging/Discharging RC circuits

High School and First Year Electricity & Magnetism

Developed by Christopher Orban

Specialized Programming Language: Javascript

### Electric Dipole in an Uniform Field

First Year Electricity & Magnetism

Developed by David Urminsky

Example Implementation: IPython/Jupyter Notebook

### Electric Field Due to a Uniformly Charged Ring

First Year Electricity & Magnetism

Developed by Aaron Titus

Example Implementation: IPython/Jupyter Notebook

### Electric Field Due to a Uniformly Charged Rod

First Year and Beyond the First Year Electricity & Magnetism

Developed by Aaron Titus

Example Implementations: IPython/Jupyter Notebook and Spreadsheet

### Equipotentials and Electric Field Lines: Collections of Point Charges and the Method of Images

First Year and Beyond the First Year Electricity & Magnetism

Developed by Jordan McDonnell

Example Implementation: IPython/Jupyter Notebook

### Lenz's Law: Induction in a Circular Loop

First Year Electricity & Magnetism

Developed by Steve Robinson

Example Implementation: VPython

### Motion of a Charged Particle in a Magnetic Field

Beyond the First Year Electricity & Magnetism

Developed by Jordan McDonnell

Example Implementations: IPython/Jupyter Notebook and Easy Java Simulations

### Particle Accelerator!

High School and First Year Electricity & Magnetism

Developed by Christopher Orban

Example Implementation: Javascript

### Solving systems of linear equations: resistor networks

First Year and Beyond the First Year Electricity & Magnetism

Developed by Eric Ayars

Example Implementations: Python, Easy Java Simulations, and Mathematica

### The Wien (E x B) Filter

First Year and Beyond the First Year Electricity & Magnetism

Developed by Ernest Behringer

Example Implementations: Python and Easy Java Simulations

### Visualizing Vector Fields and their Derivatives

Beyond the First Year Electricity & Magnetism

Developed by Michael Massa and Owen Butler

Example Implementation: Python

### Visualizing the off-axis electric field due to a ring of electric charges

First Year Electricity & Magnetism

Developed by Patrick Kelley and Gautam Vemuri

Example Implementation: MATLAB

### Relativistic Dynamics in 1D with a constant force

Beyond the First Year Modern Physics

Developed by Larry Engelhardt

Example Implementations: IPython/Jupyter Notebook, Python, and Easy Java Simulations

### Light Emission from a Finite Well: Python Root-Finding

Beyond the First Year Quantum Mechanics

Developed by Michael Burns-Kaurin

Specialized Programming Language: IPython/Jupyter Notebook

### Quantum Dynamics in 1D with a Series Solution

First Year and Beyond the First Year Modern Physics and Quantum Mechanics

Developed by Gardner Marshall

Example Implementations: Mathematica and IPython/Jupyter Notebook

### Shooting method for solving 1D quantum potentials

Beyond the First Year Modern Physics and Quantum Mechanics

Developed by Andy Rundquist

Example Implementation: Mathematica

### Spin Matrices and Linear Algebra Functions

Developed by Michael Burns-Kaurin

Specialized Programming Language: IPython/Jupyter Notebook

### Using the Finite-Difference Approximation and Hamiltonians to solve 1D Quantum Mechanics Problems

Beyond the First Year Modern Physics and Quantum Mechanics

Developed by Marie Lopez del Puerto

Example Implementations: MATLAB and IPython/Jupyter Notebook

### Density measurement and Propagation of Error

First Year Experimental / Labs

Developed by Hai Nguyen

Example Implementation: Python

### Lab Skills: Converting file formats

First Year and Beyond the First Year Experimental / Labs

Developed by Eric Ayars

Example Implementation: Python

### Projectile Motion: Experiment and Computational Model

First Year Mechanics and Experimental / Labs

Developed by Todd Zimmerman

Example Implementations: Glowscript, IPython/Jupyter Notebook, Sage Worksheet, and Easy Java Simulations

### Study of rectilinear motion with a smartphone: Elevators and Slides

First Year Mechanics and Experimental / Labs

Developed by Amador García Fuente, María Rita Sierra Sánchez, Maria Velez, and Maria Rosario Diaz Crespo

Example Implementations: Octave and Python

First Year and Beyond the First Year Mechanics and Mathematical / Numerical Methods

Developed by Steve Robinson

### Curve Fitting

Beyond the First Year Experimental / Labs and Mathematical / Numerical Methods

Developed by Eric Ayars

Example Implementation: Python

### Error Propagation

First Year and Beyond the First Year Experimental / Labs and Mathematical / Numerical Methods

Developed by Earl Blodgett

Example Implementation: IPython/Jupyter Notebook

### Monte Carlo error propagation

First Year Mathematical / Numerical Methods

Developed by Andy Rundquist

Example Implementations: Mathematica, Easy Java Simulations, and Python

### Separation of Variables in Cartesian Coordinates

Beyond the First Year Electricity & Magnetism and Mathematical / Numerical Methods

Developed by Jordan McDonnell

Example Implementation: IPython/Jupyter Notebook

### Separation of Variables in Spherical Coordinates

Beyond the First Year Electricity & Magnetism and Mathematical / Numerical Methods

Developed by Jordan McDonnell

Example Implementation: IPython/Jupyter Notebook

### Introduction to GlowScript and VPython

First Year Programming Introductions

Developed by Aaron Titus

Specialized Programming Language: Glowscript

### Introductory data analysis with Jupyter Notebooks

First Year and Beyond the First Year Experimental / Labs and Programming Introductions

Developed by Rebeckah Fussell, Megan Renz, Philip Krasicky, Robert Fulbright, Jr., and Natasha Holmes

Specialized Programming Language: IPython/Jupyter Notebook

### Lunar Lander

First Year and Beyond the First Year Mechanics and Programming Introductions

Developed by Aaron Titus

Example Implementations: Glowscript and Easy Java Simulations

### Move the Blob!

High School Mechanics and Programming Introductions

Developed by Christopher Orban

Example Implementation: Javascript

### Using Python in Introductory Physics

First Year Programming Introductions

Developed by Eric Ayars

Specialized Programming Language: Python

### 2-State Systems: Statistical Mechanics in Sports and the Story of the Purple Pandas

Beyond the First Year and Advanced Thermal & Statistical Physics

Developed by Brandon Lunk

### Boltzmann distribution, the statistical way

First Year and Beyond the First Year Thermal & Statistical Physics

Developed by Jay Wang

Example Implementations: Python and IPython/Jupyter Notebook

### Einstein Solids: Equilibrium, Temperature and Heat Capacity

Beyond the First Year Thermal & Statistical Physics

Developed by Brandon Lunk

Example Implementations: IPython/Jupyter Notebook and Spreadsheet

### Einstein Solids: Statistical Mechanics for Systems in Contact

Beyond the First Year Thermal & Statistical Physics

Developed by Brandon Lunk

Example Implementations: IPython/Jupyter Notebook and Spreadsheet

### Heat flow -- Dynamics of a 1D rod

First Year and Beyond the First Year Thermal & Statistical Physics

Developed by Larry Engelhardt

Example Implementations: IPython/Jupyter Notebook, Python, and Easy Java Simulations

### Ice thickness

Beyond the First Year Thermal & Statistical Physics

Developed by Andy Rundquist

Example Implementation: Mathematica

### Frequency Extraction via Test Functions

First Year Experimental / Labs and Waves & Optics

Developed by Peter Bryant

### Laser Beam Profile

Beyond the First Year Waves & Optics

Developed by Ernest Behringer

Example Implementations: Python and Easy Java Simulations

### Lattice Elasticity, the Vibrating String, and Nonlinearity

Beyond the First Year and Advanced Mathematical / Numerical Methods and Waves & Optics

Developed by Walter Freeman

Example Implementations: C/C++ and Easy Java Simulations

### Rainbows

First Year and Beyond the First Year Waves & Optics

Developed by Ernest Behringer

Example Implementations: Python and Easy Java Simulations

First Year and Beyond the First Year Waves & Optics

Developed by Ernest Behringer

Example Implementations: Python and Easy Java Simulations

### Wave Interference (with sound!)

First Year Waves & Optics

Developed by Christopher Orban

Example Implementation: Javascript

### Visualizing X-Ray Diffraction

First Year and Beyond the First Year Modern Physics, Waves & Optics, and Condensed Matter Physics

Developed by W. Brian Lane

Example Implementations: IPython/Jupyter Notebook and Python

### 2-Body Gravitation

First Year and Beyond the First Year Mechanics and Astronomy

Developed by Walter Freeman and Kelly Roos

Example Implementations: Mathematica, MATLAB, Python, Glowscript, and Spreadsheet

### Binary Orbit Inspirals Due to Gravitational Radiation

First Year and Beyond the First Year Mechanics and Astronomy

Developed by Robert Hilborn

Example Implementations: Glowscript and Mathematica

### Finding the Earth-Sun Lagrange Points

Beyond the First Year and Advanced Mechanics, Mathematical / Numerical Methods, and Astronomy

Developed by Nicholas Nelson

Example Implementation: Python

### Gravitational Waves from Binary Orbits

First Year and Beyond the First Year Mechanics and Astronomy

Developed by Robert Hilborn

Example Implementations: Glowscript and Mathematica

### Gravitational stability of a planet within its rings

Beyond the First Year Mechanics and Astronomy

Developed by Michael Massa

Example Implementation: Python

### Visualizing Effects of a Gravitational Wave with a Ring of Test Masses

Advanced Mathematical / Numerical Methods, Waves & Optics, and Astronomy

Developed by Deva O'Neil

Example Implementation: Glowscript

### Cliff Diving and Quadratic Drag

First Year Mechanics, Experimental / Labs, and Fluids

Developed by Peter Bryant

Example Implementations: IPython/Jupyter Notebook and Spreadsheet

### Efficiency of a Water Turbine (3D Printing Lab)

First Year Mechanics, Experimental / Labs, and Fluids

Developed by Deva O'Neil, Benjamin Hancock, and Benjamin Hanks

### Investigating Torque with 3D Printed Waterwheels

First Year Mechanics, Experimental / Labs, and Fluids

Developed by Benjamin Hancock, Deva O'Neil, and Hannah McPherson

### Pascal’s Law and the Origin of Buoyancy

First Year Mechanics and Fluids

Developed by Deva O'Neil

Example Implementation: Glowscript

### What a Drag: A Projectile Motion Game with Air Resistance

First Year and Beyond the First Year Mechanics and Fluids

Developed by Steve Robinson

Example Implementation: Glowscript

### Exoplanets: Detection via Doppler Shift (Wobble method)

First Year and Beyond the First Year Modern Physics, Waves & Optics, Astronomy, and High Energy / Nuclear / Particle

Developed by Deva O'Neil

Example Implementation: Glowscript

### A Stochastic Model of Birth-Death Population Dynamics

Beyond the First Year and Advanced Mathematical / Numerical Methods, Thermal & Statistical Physics, and Biophysics

Developed by Brandon Lunk

Example Implementations: Glowscript, IPython/Jupyter Notebook, and MATLAB