I've done some questions on RLC circuits where I have a second order differential equation of the form: [tex]L\frac{{d^2 q}}{{dt^2 }} + R\frac{{dq}}{{dt}} + \frac{q}{C} = E\left( t \right)[/tex](adsbygoogle = window.adsbygoogle || []).push({});

The solution of this equation gives an expression for the charge as a function of time, q(t). Just off the top of my head I think that the numbers(for the inductance, resistance etc) can be fudged so that the particular solution is something of the form [tex]q\left( t \right) = Rt\cos \left( {\omega t + \varphi } \right)[/tex]. In other words, the expression for long term behaviour of q(t) is a series of unbounded oscillations.

I'm not sure if this sort of thing actually happens in real life, but the math suggests that 'resonance' occurs. And I'm thinking that at least some of the 'applications' questions I've been doing have some relation to real life. I'd basically like to know if there is any physical interpretation of a q(t) with unbounded oscillations? Charge appearing from out of nowhere? I'm pretty clueless when it comes to interpreting the math. So can someone shed some light on this problem for me?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Circuits and resonance

**Physics Forums | Science Articles, Homework Help, Discussion**