Oscillating series RLC circuit

[reising1]

Homework Statement

In an oscillating series RLC circuit, with a 8.77 Ω resistor and a 15.0 H inductor, find the time required for the maximum energy present in the capacitor during an oscillation to fall to 1/8 its initial value.

Homework Equations

I know that for an RLC Circuit,

q = Qe^(-Rt/2L)cos((w')(t) + phi)

and that

U = q^2 / 2C

The Attempt at a Solution

Plugging in q, we have

U = (Q^2)(e^(-Rt/L))cos^2((w')(t) + phi)

I'm not sure where to go at this point. Ideally, I'd like to find the maximum of this function U(t), however I'm really confused about the "phi" aspect. What exactly is "phi" and what is it equal to in this case and why?

 

[ehild]

You can take the maximum of U at cos(w't+ phi) = 1. So the maximum energy is (Qe^(-Rt/2L))^2/(2C). Find the time when it falls 1/8 of the original value.


ehild