Transfer Function of a second order system
from what I recall...

Input torque \$T(t)=K_tI(t)\$

Frictional torque is \$T_f=b_m~d\theta(t)/dt\$ for viscosity b times rotational velocity  dθ(t)/dt , or sometimes Ω(t) by Mech Eng. and acceleration  d²θ(t)/dt with rot. inertia, J 

\$J~\frac{d^2θ(t)}{dt^2} = T(t) − T_f\$

Spring Torque is \$T_s=K_s*\frac{d\theta}{dt}\$

Back EMF, Vb is proportional to RPM

\$V_{emf}=K_b\frac{d\theta}{dt}\$

and Current is the difference between applied voltage and Vemf into the motor coil resistance, R at DC

\$I(t)=\frac{V(t)-V_{emf}}{R_{dc}}\$

hope that gets you started to get \$G(t)=\frac{\theta}{I(t)}\$ .... oh and gear ratio Kg=N1/N2 reduces velocity and increases torque.

Hint: current is proportional to acceleration