## Mathematics & Science
Learning Center |
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## Applications of Differential Equations## The Simple Pendulum
## An Example Involving FrictionReminder: we're dealing with the initial value problem:
We'll now put in some actual numbers for the constants in our initial value
problem. Taking
Now it's up to you to analyze this new problem in exactly the same way as we did earlier for the frictionless model. Find both: - a linsol solution representing the solution of the
**linearization**of this problem. (You must do the linearization yourself, of course, but it should be easy if you look at what we did before.) - an actsol solution, found using NDSolve
(use the interval 0 ≤
*t*≤ 10 this time, instead).
Make colored graphs of both solutions on the same plot, and do the whole analysis twice: - once for
*v*_{o}= 1 - once for
*v*_{o}= 10.
Carefully consider both graphs and decide whether they give the type of information you would expect physically. OK, time to cut you loose. You can always return here if you forget any
of the instructions, or you can look back at what you did earlier in your
We'll now go look at the |
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ODE Laboratories: A Sabbatical Project by Christopher A. Barker©2017 San Joaquin Delta College, 5151 Pacific Ave., Stockton, CA 95207, USA e-mail: cbarker@deltacollege.edu |