This paper develops a model to study the inertial dynamics of single Type 4 Wind Turbine Generator (WTG)s that emulate the response of grid-friendly Virtual Synchronous Generator (VSG)s. In this vein, a simplified linearized model is developed for the WTG in the electromechanical time scale considering complete WTG dynamics to obtain/investigate the power System Frequency Response (SFR) characteristics. The objectives are to obtain virtual frequency motion equation, present the mechanism of inertia provision clearly, and feature physical interpretations of inertial frequency response. Accordingly, the available inertia constant and damping coefficient are estimated/expressed analytically in frequency-domain that synthetically embed the impacts of key control parameters as well as the initial operating points. It is realized that the available inertia constant and damping coefficient are adjustable and frequency dependent in contrast to that's manifested by a conventional synchronous generator. The developed virtual frequency motion equation is used in turn to establish/investigate the complete SFR model of a generic test power grid which features enormous wind power generation capacity factor. The theoretical analysis shows that the SFR attributes could get adjusted/enhanced by proper tuning of the WTG control parameters. Comprehensive and comparative time domain simulations are also performed in the MATLAB/Simulink platform. It is to verify the accuracy of the proposed models in the evaluation of SFR characteristics and authenticate the theoretical analysis.