# Second order circuit with 2 capacitors to differential equation

1. Jan 26, 2012

### nicksname

hello i need help with this,

what is the differential equation for the voltage v2 (t).

http://www.imageurlhost.com/images/mc2qqp4kax37kvm51h1h_circuit.jpg

sorry for my english

2. Jan 26, 2012

### tiny-tim

welcome to pf!

hello nicksname! welcome to pf!

show us what you've tried, and where you're stuck, and then we'll know how to help!

3. Jan 26, 2012

### nicksname

i know how it works with inductors. to find differential equation v with KVL (Kirchhoff's current law). but I've never done it before for the capacitor to v2(t). writing. i know I need to use Kirchhoff's voltage law. but that it is.

4. May 7, 2012

### ShamelessGit

Gah I need help with a similar problem and it's frustrating that it's not solved yet. I know how to substitute when there's an inductor and a capacitor, but it beats me how to do it when the energy savers are both the same circuit element.

So far I've got 2 helpful mesh equations (my problem has 3, but i used the last one to define the currents in terms of voltage derivatives) and I've replaced all the currents by Cdu/dt, but I don't know what to do next to get rid of the du/dt for the first capacitor. It looks like I could cancel out the Uc1s by substituting the equations into each other, but I need some other equation that I can't think of yet for the first du/dt I mentioned.

5. May 7, 2012

### HallsofIvy

You may have two different currents in the two lower wires so you should set up two first order differential equations describing those. If you are required to have a single equation, you can combine those into a single second order equation for for either one of the currents.

6. May 7, 2012

### ShamelessGit

I don't think that can be done because there will be two functions in each of the differential equations.

7. May 7, 2012

### ShamelessGit

I think I figured it out. When I did it (my problem has an extra loop, so you might have to do something slightly different), after I substituted everything I could I ended up with two mesh equations both in terms of V1, V2, dV2/dt, and one had dV1/dt, and then got stuck for a while. But then I figured out that you could solve the equation that did not have dV1/dt in it for V1, then I derived it to get another equation which put dV1/dt in terms of only V2 and dV2/dt. That gave me enough equations to solve the rest of the problem using only algebra.