For a certain problem the transfer function was given as 2s6

For a certain problem the transfer function was given as 2s+6/s^2 + 3s + 2 Compute: Damping ratio. Natural frequency If a step input was applied to this system would the response be underdamped, overdamped or critically damped?

Solution

2*zeta*wn= 3 and wn^2= 2 => wn= sqrt(2) =1.414

zeta= 3/(2*1.414)=1.06 is damping ratio

wn= natural frequency=1.414

zeta> 1 system is over damped

when a pole at origin is introduced into a system i.e, stsady state error for step input gives a constant value =3

that is there will be deccrease in damping ratio resulting to be critially or under damped