I have been attempting to solve the problem attached (question 1). I am however stuck on getting an expression for the natural frequency. Please help in this regard. My attempt is also attached.

 

... something is not quite right with your fractional multiplication. Try multiplying numerator and denominator by the s(s+1) factor.
... You are given the percent overshoot. You can find a formula for \(\zeta\), given PO ... ought to be in the text.

 

I have been attempting to solve the problem attached (question 1). I am however stuck on getting an expression for the natural frequency. Please help in this regard. My attempt is also attached.

Hello,

I agree with the previous post in that your math is not correct when calculating Gs/(1+Gs*Hs).
Try that again and if successful you will see the right constant in the denominator which represents w^2.

Also, the diagram was extremely hard to read. Here is a better diagram.