This paper focuses on the state space modeling approach and output torques prediction of torsional vibrations for variable speed wind turbines. The multi-body system model under study is mainly comprised of a wind turbine, a three stage planetary gear box and an induction generator. The masses-springs approach of shaft system differential equations is developed from Newton's law and Lagrange formulas. For an easy comprehension for electrical engineers and tutorial purpose, an electrical equivalent circuit of the system is proposed by using mechanical and electrical components similarities. Extensive numerical simulations are performed to investigate system mechanical resonances and impacts of damping factors on the system dynamic and stability.