Which of the following transfer function Gsim s can be used

Which of the following transfer function G^sim (s) can be used for describing dynamic response of a fixed-displacement vane pump?________. G^sim(s) =k_v(1+tau_i s)/[s/omega_n)^2 + 2 zeta [s/omega_n] +1 G^sim(s) =k_v(1+tau_i s)/[s/omega_n)^2 + 2 zeta [s/omega_n] +1 G^sim(s) =k_v/(1+s tau_i)/[s/omega_n)^2 + 2 zeta [s/omega_n] +1 G^sim(s) =k_v(1+tau_i s)/[s/omega_n)^2 + 2 zeta [s/omega_n] +1 where s is Laplace operator and k_v is pump coefficient, xi is pump damping ration, omega_n pump natural frequency, and tau_i pump time constant respectively.

Solution

this is partly usefull

http://etd.library.vanderbilt.edu/available/etd-09222008-104852/unrestricted/Dissertation_LiBo.pdf