Specialized MATLAB material developed by Gautam Vemuri and Andy Gavrin - Published November 24, 2020
|Levels||First Year and Beyond the First Year|
• Convert 2nd order ordinary differential equation (ODE) to a pair of coupled 1st order ODEs for numerical implementation (Exercise 1). • Solve the equation of motion for a pendulum, both with and without the small angle approximation, by using Euler-Cromer integration (Exercise 1). • Determine the period of an oscillatory function numerically, e.g., by counting peaks (Exercise 2). • Solve the equation of motion for a damped pendulum, both with and without the small angle approximation, by using MATLAB’s ODE45 differential equation solver (Exercise 3). • Make and interpret phase plots (Exercise 3). • Use MATLAB’s ODE45 differential equation solver to solve the damped, driven oscillator, and to explore the properties of the solution (Exercise 4). • Use Euler-Cromer integration to find the motion of a nonlinear oscillator with restoring force given by F = -kx^3, and show that its period is inversely proportional to its amplitude. (Exercise 5). • Evaluate the range of validity of an approximation. • Use a numerical solution to qualitatively explore the behavior of a complex system. • Use a numerical solution as an experimental platform from which they can extract and analyze data.
|Time to Complete||120 min|
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Credits and Licensing
Gautam Vemuri and Andy Gavrin, "Physical Pendulum without Small Angle Approximation," Published in the PICUP Collection, November 2020, https://doi.org/10.1119/PICUP.Exercise.PWSAA.
The instructor materials are ©2020 Gautam Vemuri and Andy Gavrin.
The exercises are released under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 license