Our lecturer request us to find the value of gain,K that have (for close loop)

-Settling Time less than 8s

-Overshoot less than 40%

I had already figure out the value of zeta(damping ratio) by using the 2nd order system of Maximum Overshoot equation which is = 2.8, and how do i figure out the value of Wn( frequency) because when i use the 2% criterion to calculate it, it provide me the value of 1.7864(Why it is different with the freq i find in MATLAB) and how do i use this 2nd order approximation to recover back to find the value of gain K in 3rd order.

Characteristic equation of 3rd order closed loop:s^3+26s^2+125s+(100+K)

ps. I had use MATLAB to figure out the gain(using 3rd order cloose loop transfer function), value should be about K=860, and with damp ratio 2.8 and freq of 6.54rad/s

sorry for my broken english and thx for helping