Hello again normad,
Ok, sorry about that, i didnt understand your question. Now that i do, i understand fully what you are talking about and i think we can finally resolve this discrepancy.
What happened was when ljcox did the original op amp analysis, he apparently did not get the polarity right. The output is negative with respect to the input so the equation has to be written with the inversion caused by the op amp in mind. This leads to a totally different equation really, so we would have to go back to the beginning and start over again.
I guess it is partly my fault too because i did not check his previous work first, but followed after that.
We have to start like this:
Vi/r=-Vo/R-dVo*C
and if you compare with previous results, you'll see that the Vo terms all have to be negative to account for the inversion by the op amp. The effect is that the input gets inverted, so we end up with this:
Vo=(w*cos(w*t)*C*R^2-sin(w*t)*R)/(r*w^2*C^2*R^2+r)+K*e^(-t/(R*C))
where
K=-(w*C*R^2)/(r*w^2*C^2*R^2+r)
and now if you compare that to the simulation you are doing you should find it to be EXACTLY the same.
Again im sorry about the misunderstanding, and im sure ljcox will want to go back over his work and see what had happened.
I'll leave it to you to solve for the above equation following the same guidelines as we did before, just starting out with the Vo terms negative.
If you cant get it for some reason just yell and we'll go over it again, no problem. I think it is interesting to do the phase shift and offset too but of course we dont have to.