How does feedback affect the transfer function of an integrating block?

[Setareh7796]

Homework Statement

Finding the transfer function

Relevant Equations

I have written my solution in the pic attached.

The correct solution is different than my answer, I am not sure where I am going wrong?

 

[cnh1995]

Your answer is correct considering the block diagram you have drawn.
Did you construct the block diagram on your own using the data in the problem or was the block diagram already given in the problem?

If you developed it on your own, you need to post the exact question here to verify if your block diagram itself is correctly drawn as per the given data.

 

[LvW]

Yes - correct answer. The block diagram shows an integrating block with feedback (proportional).
This gives a lowpass response - which is in agreement with your formula (in blue).
The red one is wrong - a first oder block with P-feedback cannot give a 2nd-order functioin.