Solving for Vo: Nodal Analysis Approach

[eehelp150]

Homework Statement

Determine the output voltage Vo(t) in terms of Vs

Homework Equations

The Attempt at a Solution

If I were to use Nodal Analysis to solve this, would these be the proper nodal equations?$$\frac{V1}{-j1.6} + \frac{V1-Vs}{175} = 0$$
$$\frac{V_{I2}-Vo}{10k} + \frac{V_{I2}}{1k} = 0$$

 

[gneill]

Sure, those would be a good start.

 

[eehelp150]

Sure, those would be a good start.

Is V1 = V2?

 

[gneill]

Is V1 = V2?

Well, it's an ideal op amp with feedback to the negative input. So that would be a yes.

 

[eehelp150]

Well, it's an ideal op amp with feedback to the negative input. So that would be a yes.

I end up with:
j25.45Vo + 0.233Vo = 2.56Vs
Does this look good so far?

 

[gneill]

I think that looks okay. Hard to tell without seeing the full derivation, but it certainly yields a result for Vo that's almost spot on compared to what I calculate.

 

[eehelp150]

I think that looks okay. Hard to tell without seeing the full derivation, but it certainly yields a result for Vo that's almost spot on compared to what I calculate.

How far off am I compared with your results?

 

[gneill]

How far off am I compared with your results?

Within plausible rounding error range. The expression you provided was not in a typical final form, since Vo was not isolated. So I "solved" it for Vo in terms of Vs and compared the proportionality constant with what I derived. Here: