arXiv:2610.22572v1 Announce Type: new Abstract: The periodic power demand of large data centers can introduce forced oscillations into the power system. When these oscillations contain frequency components near a turbine-generator torsional mode, they may excite sustained shaft torque oscillations with amplitudes exceeding the allowable cyclic torque limits. Characterizing the impact of data center power oscillations on generator shaft torque requires accounting for frequency-dependent network coupling among the data center, the transmission network, and the generators. Although electromagnetic transient (EMT) simulations can capture these interactions in detail, repeated simulations across excitation frequencies and load locations can be computationally demanding. This paper proposes an analytical framework for data center induced torsional oscillations that retains the coupled electrical and shaft dynamics. A detailed generator-network model is established, and closed-form transfer functions that map data center power perturbations to the torque in each shaft section are derived. Admissible shaft torque amplitudes are then translated into frequency-dependent limits on data center power oscillations. The proposed framework enables fast assessment of the shaft torque response while accounting for network dynamics and provides a quantitative screening criterion for candidate data center connection buses. The framework is validated on the IEEE benchmark model and applied to the IEEE 39-bus system.