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## Homework Statement

Find the charge on the capacitor in an L-R-C circuit at time t = 0.001

L = 0.05H, R = 2 ohms, C = 0.01F

q(0) = 5

i(0) = 0

E(t) = 0

## Homework Equations

## The Attempt at a Solution

[tex] L \frac {di(t)}{dt} + R \frac {dq(t)}{dt} + \frac {q}{C} = 0 [/tex]

[tex] \frac {dq^2(t)}{dt^2} + \frac {R} {L} \frac {dq(t)}{dt} + \frac {q}{LC} = 0 [/tex]

[tex] \frac {dq^2(t)}{dt^2} + 40 \frac {dq(t)}{dt} + 2000q = 0 [/tex]

[tex] m^2 = 40m + 2000 = 0 [/tex]

[tex] q(t) = e^{-20t} (c1 * cos(40t) + c2 * sin(40t)) [/tex]

q(0) = 0 yields c1 = 5

[tex] q'(t) = i(t) = -20e^{-20t} (c1 * cos(40t) + c2 * sin(40t) ) + e^{-20t}(-200 sin (40t) + 40*c2*cos(40t))[/tex]

c1 = 5

c2 = 5/2

I get q(0.01) = 4.11 coulombs

The book has q(0.01) = 4.568 coulombs

Can you help resolve my error?

Thanks

-Sparky_

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