## Applications of Differential Equations

### Preliminary Example

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Using Mathematica as a simple calculator you should have gotten:

(0-10*0-1/0.001)/0.25

-4000.

So our second initial condition now becomes I'(0) = -4000. At last we have a workable initial value problem, namely:

L I'' + R I' + I/C = E'

I(0) = 0

I'(0) = -4000

Have Mathematica solve it for you, assigning the result into the variable underdamped. Remember I is a reserved Mathematica constant, so you'll have to use i to represent current instead. Also, don't forget to plug in the correct values for L, R, C, and E' (thats E prime not just E), and make the independent variable t, not x. (Obviously in this case, since E(t) = 0, then E'(t) = 0.)

Switch back to Mathematica now and get on with it!

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

 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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