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## Homework Statement

A 2-[tex]\mu F[/tex] capacitor is charged to 20 V and then connected across a 6-[tex]\mu H[/tex] inductor forming an LC circuit.

(a) Find the initial charge on the capacitor

(b) At the time of connection, the initial current is zero. Assuming no resistance, find the amplitude, frequency and phase of the current. Plot the graph of the current versus time.

## Homework Equations

I was able to get part (a) no problem. It's simply:

[tex]Q = E_{c}C[/tex] where [tex]E_{c}[/tex] = Voltage drop

Relevant equation for part (b):

LdI/dt + Q/C + RI = E

I = dQ/dt

LI" +RI' + I/C = dE/dt

L is the inductance.

## The Attempt at a Solution

The second order differential equation's solution should be of the form

y = acost(wt) + bsin(wt).

you can divide through by L to get:

I" + RI'/L + I/(LC) = dE/dt(1/L)....since R = 0

I" + I/ (LC) = dE/dt(1/L)

I set the right side equal to zero and was able to get a for the solution equation, but couldn't get b. I am not sure how to proceed now. I realize I can't just use 20V for E because that's just for the capacitor, not the whole circuit. Thanks for your help.