Second Order Op Amp circuit: Find Vo for t > 0

[VinnyCee]

Homework Statement

In the circuit below, determine v_o(t) for t > 0. Let V_{IN}\,=\,u(t)\,V, R_!\,=\,R_2\,=\,10\,k\Omega, C_1\,=\,C_2\,=\,100\,\muF.

http://img249.imageshack.us/img249/3840/problem867cg5.jpg

Homework Equations

i_c\,=\,C\,\frac{dv_c}{dt}

The Attempt at a Solution

Add some node voltages:

http://img413.imageshack.us/img413/2935/problem867part2vn2.jpg

KCL @ V_1:

\frac{V_{IN}\,-\,V_1}{R_1}\,=\,C_2\,\frac{dv_2}{dt}\,+\,C_1\,\frac{dv_1}{dt}

KCL @ V_2:

C_2\,\frac{dv_2}{dt}\,=\,\frac{V_2\,-\,V_o}{R_2}

Substituting for \frac{dv_2}{dt} in the KCL @ V_1 equation:

V_o\,=\,-R_2C_2\left(\frac{V_{IN}\,-\,V_1}{R_1C_2}\,-\,\frac{C_1}{C_2}\,\frac{dv_1}{dt}\right)

Now what do I do to solve?

 

[berkeman]

Set V2 and dV2/dt = 0. Does that help?