# 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

Staff Emeritus
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.