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An analytical model is developed to describe the torsional responses of the powertrain system. The model is used to analyze system equilibrium, free vibration, forced and self-excited vibrations. The equations of motion are linearized about the equilibrium to determine natural frequencies and mode shapes of the torsional modes. The forced responses of the system are investigated by including the excitations of gas combustion forces and inertia torques induced by the reciprocating motions of the piston and connecting rod. The self-excited vibration induced by negative damping behavior of clutch torque capacity is studied. For an example rear-wheel drive powertrain considered, the free vibration analyses show the natural frequencies and the associated mode shapes. The forced and the self-excited vibrations for the transmission gearset and the driveline components are examined. Experimental measurements from a test powertrain are used to confirm the theoretical predictions.