This question is more about math than anything, but it comes up in LRC frequency analysis so much that if anyone knows it, its you guys. I am trying to find the values of a resistor, capacitor and inductor. The only knowledge I have is that the three elements are connected in series and the output voltage is taken across the capacitor. Input voltage is just V(t) no value. But it will cancel. I do know the transfer function H(s) for the circuit. So I use voltage division, solve for V output, V input cancels, and I end up with my own expression for the transfer function. Now I need to compare them. This is not homework, this comes up all the time in my circuits class and I never encountered a situation where I don't know anything at all except the transfer function before, until now. Here is the known transfer function. 1/ (s^2+ sqrt(2)*s +1) Here is the transfer function expression I came up with using the process above. 1/ (L*C*s^2+ R*C*s+1) So pretty much 1= LC and sqrt(2) = RC The problem is that there are a million combinations of values of L and C that will give you 1, and R and C that will give you sqrt(2). So how the heck do I find the values of R L and C? I tried to use the fact that both expressions have C as a common factor, but I'm not sure how. System of linear equations could work here, but also not sure how. Anyway please help. Its probably very easy, but I'm not sure how to do it. Thank you.