- #1

oldthrall

- 3

- 0

## Homework Statement

I have uploaded the questions in the attachment. I am having trouble with 2. e,f and 3.c

untitled.png is the parts that I am having trouble with. untitled1.png and untitled2.png is the entire question.

## Homework Equations

y(t)= steady state+transient

## The Attempt at a Solution

For part E I have tried to change x(t) into a phasor and so according to the question x(t) becomes A. Then letting X=A, and then subbing in ω=1/RC I got Y/X=2, then finally Y=2A...

The problem I have is I don't know how to get from that part to calculating the peak current. There was an earlier part of the question which asked me to derive the transfer function, and I did so by writing out the KCL equations for V1,V2,V3 using a common voltage V and assuming V+=V- and that the op-amps are ideal. I wonder if the approach to this question is using the KCL equations for the V1/V2/V3 nodes and subbing in X=A for them? But then I don't know what to do with the unknown R and C

for part f I am confused because I worked out the corner frequency earlier to be ω=1/RC and so using the transfer function, where Y/X=2 when you sub in ω=1/RC and on the right I sub in ω=2∏1000. I attempted to separate imaginary and real parts so that I can find the real parts to be the R value and imaginary the capacitance, but then in the end the terms with RC cancel out and I'm left with something that doesn't make sense.

Then for part C I earlier worked out the steady states for both open and closed. The steady state for open was y(t)=2.8cosωt+0.89sinωt and for closed it was 4.49cosωt+2.8sinωt. When the transient amplitude is equal to zero, that means when the the y(t0) is equal to the steady state when the circuit is closed right? So I now have y(t0)=4.49cosωt0+2.8sinωt0+Ae^(-t0/τ) where τ is the time constant and A here is the transient amplitude, which is equal to zero. But since I don't know what t0 is how can I find out what y(t0) is?

Thanks!

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