1. The problem statement, all variables and given/known data This is to look at the effect of damping on the frequency of a series RLC circuit. Let W=1/(sqrt(LC)) be the frequency of an undamped circuit. Suppose enough resistance is added to bring Q down from infinity to 1000. By what percentage is the frequency, ω, thereby shifted from W? 2. Relevant equations 3. The attempt at a solution So, I know that ω=sqrt(W^2-(R/2L)^2). I can pull out the W, and say ω=W[1-(R/(2LW))^2]^(1/2). I think I can justify that fraction being small, because let's just assume that the R I added was small (Q is 1000, which is quite large, so that's a fair assumption). Then I'll use a binomial expansion to say that ω≈W[1-(R^2/(8*L^2*W^2)]. But now I'm stuck: I know that Q=ω*L/R=1000. So, W[1-(R^2/(8*L^2*W^2)]*L/R=1000, but who do I solve this as a percentage of ω? Or have I made a mistake?