I think I have the first few portions of this question correct, but I am unsure if I have the correct answer for the portion with the sin wave.

Is what I'm doing correct?

 

It's kind of obvious. The point is that you have already calculated the values of R & C that give unity gain at 1krad/sec. So the output magnitude at 1000 rad/sec will be 2V. There will be a phase difference.

Like all things electrical there will always be strange behavior that crops up from time to time. Depending at what point (time-wise) in the AC cycle you apply the input to the integrator you get a different result with respect to the transient behavior. Do you know what the difference might be?

 

Is what I'm doing correct?

BTW - Your answers are correct.

 

BTW - Your answers are correct.

Here's the solution they are giving in the manual.

It looks like my answer would be equivalent to theirs if I hadn't had that -2 trailing my cosine term. Is that -2 accounted for somewhere or did I make a mistake?

Like all things electrical there will always be strange behavior that crops up from time to time. Depending at what point (time-wise) in the AC cycle you apply the input to the integrator you get a different result with respect to the transient behavior. Do you know what the difference might be?

Actually know that I think about it more, if I apply the signal at a time t1= pi and go to time t2 = t then the -2 goes away, right? Is this correct?

 

The constant term in the solution is a DC offset in the output. As you observed, this offset can be removed by changing the phase of the input. In fact if you make the input a simple cosine, rather than a sine function, the offset vanishes.

 

The constant term in the solution is a DC offset in the output. As you observed, this offset can be removed by changing the phase of the input. In fact if you make the input a simple cosine, rather than a sine function, the offset vanishes.

So having there negative 2 there is okay, right?

 

So having there negative 2 there is okay, right?

I have already said that your answer is correct - what more can I say?