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.
I know that for an RLC Circuit,
q = Qe^(-Rt/2L)cos((w')(t) + phi)
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?