Mathematics & Science Learning Center
Computer Laboratory

Applications of Differential Equations

Electric Circuits

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...

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