Bore hole drilling is a growing activity driven by the need to access important resources like ground water and fossil fuels. In the process, however, undesired vibrations and shocks on the drill strings are invariably experienced, and this has a detrimental impact on the equipment. To get a full understanding of the origins and characteristics of this dysfunction, a generalized lumped-parameter model of the drill string system is studied to provide a deeper understanding of the drillstring dynamics and bit mechanics. The torsional stick-slip vibration phenomenon focuses on analyzing the source of vibration excitation, which is primarily the nonlinear bit-rock fictional interaction. The impact of various parameters such as the weight on the bit, rotational speed, and damping on the severity of vibration, in particular stick-slip vibration, is further analyzed. The simulation results highlight the significance of the key factors for stick-slip onset and severity. These controllable factors can be used to eliminate stick-slip while avoiding other undesirable effects, achieving optimum performance. Further research will be done on multi-stability analysis to define the optimum operation zones and design of vibration reduction tools and control strategies.