What's the right approach to determining the step response and source free response of the attached circuit? I've attempted to do KCL (usual 1st order analysis) at v1, v2, and v3, but it looks quite messy.

 

What's the right approach to determining the step response and source free response of the attached circuit? I've attempted to do KCL (usual 1st order analysis) at v1, v2, and v3, but it looks quite messy.

I assume you're not using laplace transforms yet? Either way this is a fairly simple circuit. Everything is in series. You just need one equation. Yes, you use KCL:

Vs = I*(R1+R2) + (1/c1+1/c2)*Integral(I*dt)

Solve the equation (natural response + homogeneous response) and get your I.

After that it's easy enough. Now, I'm assuming the drawing might be off or something, because voltage is supposed to be measured between a positive and a negative terminal, but either way it's something like this:

V1 = I * R1
V2 = 1/C1 * Integral (I * dt)
V3 = I * R2

Hope this was helpful,
-blazed

 

That was helpful, thanks. I'm a little rusty, but I worked it out with your answer.

 

That was helpful, thanks. I'm a little rusty, but I worked it out with your answer.

You welcome. Glad to have been of help...

-blazed