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
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85 Exercise Sets

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3 body problem - Code for visualization of 2D Earth-Moon-3rd body trajectories

First Year Mechanics

Developed by Fabio Daniel Saccone

Example Implementation: IPython/Jupyter Notebook

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

Example Implementations: Glowscript and Spreadsheet

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

Advanced Mechanics

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

Advanced Quantum Mechanics

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

Bead on a Wire

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

Developed by Steve Robinson

Example Implementations: Glowscript and Spreadsheet

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

Pair-Programming: Variables, Vectors, and the Programming Environment

First Year and Beyond the First Year Programming Introductions

Developed by Katrina Hay and Bret Underwood

Example Implementation: MATLAB

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

Example Implementations: Python and Spreadsheet

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

Example Implementation: Spreadsheet

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

Shadows (Ray Optics)

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