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Applications of Differential Equations

The Simple Pendulum

(continued from last page...)

I'm not even going to tell you what you should have gotten. If you're paranoid, compare what you got with how you treated linsol earlier in the session.

How Good is the Linearized Solution?

The two solutions that we've found so far are a little hard to compare with one another. We solved the actual initial value problem:

y'' + 9.8 sin(y) = 0
y(0) = yo
y'(0) = vo

and got actsol in the form:

Actual Solution

We also solved the linearized initial value problem:

y'' + 9.8 y = 0
y(0) = yo
y'(0) = vo

and got linsol in the form:

Linearized Solution

So what should we do to compare these two completely different looking solutions with one another?

In order to get a better insight into both solutions we could graph both linsol, and actsol on the same coordinate system using the Plot command, on the interval 0≤t≤15. We also should color the two graphs so that we can tell which is which. We'll stick with the colors we've been using throughout the laboratory so far—red for actsol, and blue for linsol.

The command you'll need is:

Plot[{linsol,actsol},{t,0,15},
  PlotStyle->{RGBColor[0,0,1],RGBColor[1,0,0]}]

Go to Mathematica now and enter the command. (Or copy and paste from here if you're feeling lazy.)

Welcome back. Let's go see what you should have gotten...


Compass If you're lost, impatient, want an overview of this laboratory assignment, or maybe even all three, you can click on the compass button on the left to go to the table of contents for this laboratory assignment.
 
 

ODE Laboratories: A Sabbatical Project by Christopher A. Barker

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