# What is the equation of this simple R-(L||C) circuit ?

#### silv3r.m00n

Joined Apr 15, 2010
51
Here is a very simple circuit with a resistance in series with a parallel LC tank.

http://tinyurl.com/vps3e2n

All that i want to know is the equation of Vo.
I tried fiddling with it and came up with this after a lengthy derivation

Code:
Vo = Vs/(R.C.w) * { e^(-t/2.R.C) } * sin(wt)

w = 1/sqrt(LC)
Vs/(R.C.w) => Amplitude Component
{ e^(-t/2.R.C) } => Exponential damping component
sin(wt) => oscillation component
somebody tell me if that is correct ... or point me the right direction if its not.
i was looking online to find the solution, but found nothing.