Mathematics & Science Learning Center
Computer Laboratory
Applications—Simple Pendulum
CONTENT GUIDE for PENDULUM LABORATORY
General Introduction
Linearization & Solving with
Mathematica
Setting up the IVP & Justifying the Linearization Graphically
Results of Graph & Justifying Linearization Using Series
Results of
Series
& Intro. to Solving the Linearized IVP
Solving the Linearized IVP with
DSolve
Results of
DSolve
& the
[[1,1,2]]
trick
Finding the Actual Solution Numerically with
Mathematica
Solving the Actual IVP with
NDSolve
Results of
NDSolve
& the
[[1,1,2]]
trick
How Good is the Linearized Solution?
Comparing the Plots of Both Solutions
Results of Plotting & Considering Larger
y
-values
Results of Larger
y
-values & Zooming In
Results of Zooming In &
Really Large
y
-values
Results of
Really Large
y
-values & Discussion
A
Real
Pendulum: Facing Up to Friction
Deriving the Friction Aware IVP
Exercises on the Friction Aware IVP
Results of the Exercises & Final Discussion
Main Table of Contents for All ODE Laboratories
ODE Laboratories: A Sabbatical Project by Christopher A. Barker
©2009 San Joaquin Delta College, 5151 Pacific Ave., Stockton, CA 95207, USA
e-mail:
cbarker@deltacollege.edu