Computational Problems by Topic
Computational Problems by Topic
Page Created: July 2024; MLX stands for Matlab's live script .mlx files
Check home page for instructions on how to download the files on your machine
This page contains a compilation of all computation problems. They are ordered by course, starting from a small course number and going up. Within the course sequence, problems are ordered approximately following the flow of the course. Use the page search feature to more quickly find a specific problem.
Matlab Starter
(Last update: July 2024)
Learning Outcomes: Students demonstrate that they have MATLAB installed and working, could write and document basic MATLAB live scripts, and could Find help for writing code using MATLAB help resources
tag: 3605
Problem PDF Problem TEX PDF for TAs TEX for TAs MLX Solution PDF
Chi-squared Fitting
(Last update: July 2024)
Learning Outcomes: χ2 fitting of a straight line, Writing MATLAB functions, Estimating χ2 by eye.
tag: 3605, Fitting, Statistics
Covariance
(Last update: July 2024)
Learning Outcomes: Calculate covariances
Tags: 3605, Statistics
Correlation Coefficients
(Last update: July 2024)
Learning Outcomes: Calculate correlation coefficients
Tags: 3605, Statistics
Exponential Fitting
(Last update: July 2024)
Learning Outcomes: Transforming a non-linear to a linear fit, Practice the use of MATLAB functions
Tags: 3605, Fitting, Statistics
Mean and Error on the Mean
(Last update: July 2024)
Learning Outcomes: Weighted mean, error on the mean, error on the weighted mean.
Tags: 3605, Statistics
Poisson and Normal distributions
(Last update: July 2024)
Learning Outcomes: Program a Poisson and Normal distributions and use them to approximate experimental data, Calculate cumulative probability for a normal distribution, Use a bar graph, Read data from a file.
Tags: 3605, Statistics
Power Law Fitting (2 problems)
(Last update: July 2024)
Learning Outcomes: Understand how to fit to a power law by transforming to a linear fit, Interpret context-rich problems.
Tags: 3605, Statistics, Fitting
Finite Difference
(Last update: December 2024)
Learning Outcomes: Solve a first order differential equation using finite differences
Tags: 4001, Mechanics, Differential Equation
Drag Force
(Last update: July 2024)
Learning Outcomes: Solve differential equations using Matlab’s ODE45, Practice proper plotting, Using Matlab help pages.
Tags: 4001, Mechanics
Turbulent and Laminar Flows
(Last update: Decenmber 2024)
Learning Outcomes: Identify regimes of laminar and turbulent flows, Gain experience in using log-log plots to display the behavior of a physical system over a large dynamic range, Gain experience with plotting and presentation
Tags: 4001, Mechanics, Drag Force
Numerical Accuracy and Second Order Differential Equation
(Last update: December 2024)
Learning Outcomes: to practice the use of a ‘for’ loop; to use ODE45 to solve a second order ODE; to assess the role of accuracy in solving differential equations numerically.
Tags: 4001, Mechanics, Numerical Accuracy
Problem PDF Problem TEX Solution PDF Solution MLX MLX Template for Students
Coupled First Order Differential Equation
(Last update: December 2024)
Learning Outcomes: Solve two coupled first order differential equations.
Tags: 4001, Mechanics, Differential Equation, Drag Force in 2D
Effect of Drag on the Trajectory
(Last update: December 2024)
Learning Outcomes: To study the effect of drag on the trajectory of an object; To practice solving a second order, coupled ODE.
Tags: 4001, Mechanics, Differential Equation, Drag Force in 2D
Skateboarder on a Half Circle
(Last update: December 2024)
Learning Outcomes: Solve and analyze a pendulum or harmonic oscillator without a small angle approximation; Use ODE45 to solve a second order ODE.
Tags: 4001, Mechanics, Harmonic Oscillator or Pendulum, Second Order Differential Equation
Damped Oscillator
(Last update: July 2024)
Learning Outcomes: Observe the behavior with time of a damped one-dimensional oscillator; Program a mathematical equation of motion while accounting properly for initial conditions; Gain experience with plotting and presentation; Use a ‘for’ (loop or a function)
Tags: 4001, Mechanics, Harmonic Oscillation, Damping
Lagrangian and Equilibrium
(Last update: November 2024)
Learning Outcomes: Work with energy diagrams; Gain experience with the Lagrangian formulation; Find small angle solutions near a stable equilibrium
Tags: 4001, Mechanics, Lagrangian, Equilibrium
Lagrangian with Cosh Potential (Quiz)
(Last update: July 2024)
Learning Outcomes: Write the Lagrangian for an oscillating system, Find the frequency of small oscillation, Solve the equation of motion numerically using initial conditions
Tags: 4001, Mechanics, Lagrangian
Lagrangian and Solving Differential Equations
(Last update: November 2024)
Learning Outcomes: Solve differential equations numerically to obtain an exact solution; Observe the exact solution of small perturbations near an equilibrium; Integrate a numerical solution; Convert from polar to Cartesian coordinates
Tags: 4001, Mechanics, Lagrangian, Equilibrium, Differential Equations
Rigid Rod Pendulum (Quiz)
(Last update: November 2024)
Tags: 4001, Mechanics, Lagrangian, Euler-Lagrangian Equation of Motion, Equilibrium, Small Oscillation
Fourier series
(Last update: November 2024)
Learning Outcomes: Work with Fourier series expansion, Understand the relation between the force's Fourier components and the displacements
Tags: 4001, Mechanics, Fourier series
Oscillations
(Last update: November 2024)
Learning Outcomes: Solve a problem with coupled oscillators
Tags: 4001, Mechanics, Oscillations, Normal modes
Multi-stage Rockets
(Last update: November 2024)
Learning Outcomes: Solve the rocket equation with constant gravity; Practice with multi-stage rockets; Illustrate the importance of fuel fraction and burn rate; Make plots to visualize some of the physics
Tags: 4001, Mechanics, Momentum Conservation, Multi-stage Rockets
Rocket with Variable Gravity and Drag (Exam)
(Last update: November 2024)
Tags: 4001, Mechanics, Momentum Conservation, Rocket, Drag Force, Variable Gravity
Moment of Inertia
(Last update: November 2024)
Learning Outcomes: Calculate the center of mass and moment of inertia (MOI), Diagonalize the MOI tensor and find principal axes and moments numerically, Use normalized quantities, Visualize the principal axes relative to the body, Practice the relation between angular momentum and angular velocity
Tags: 4001, Mechanics, Moment of Inertia, Principal Axes, Angular momentum
Coriolis Force
(Last update: November 2024)
Learning Outcomes: Expand your knowledge of working with differential equations; Gain more insight about the magnitude of the effects due to Earth’s rotation
Tags: 4001, Mechanics, Coriolis Force, Rotation, Non-inertia frame, Differential Equation
Quadratic Map
(Last update: November 2024)
Learning Outcomes: Solve a non-linear differential equation using iterations, Display the behavior of decaying solutions and of solutions with fixed points
Tags: 4001, Mechanics, Quadratic Map
Standing Wave
(Last update: November 2024)
Learning Outcomes: Find the eigenvectors and eigenmodes of a two-mass oscillating system, Generalize the two-mass matrix problem to larger dimensions and visualize the physical behavior
Tags: 4001, Mechanics, Lagrangian, Euler-Lagrange Equation, Eigenvalues and Eigenmodes, Standing Wave
Masses Connected by Springs (Quiz)
(Last update: November 2024)
Tags: 4001, Mechanics, Lagrangian, Euler-Lagrange Equation, Eigenfrequencies and Eigenmodes
Damped Driven Pendulum (Exam)
(Last update: November 2024)
Tags: 4001, Mechanics, Lagrangian, Drag, Driven Force, Non-linear behavior, Fixed points