This paper provides an analysis of one of the dysfunctions in borehole drill strings, which is torsional vibration. Additionally, an analysis of mitigation through systematic adjustment of the key parameters of Weight on the Bit (WOB) and Rotations per Minute (RPM) is conducted. One of the key forms of dysfunction is undesired vibration and shocks on the drill strings. The vibration and shock experienced by drill strings have a detrimental impact on equipment life, resulting from damage to the drill bit and the drill string components. This paper studies a generalized lumped-parameter model of the drill-string system to provide a fundamental understanding of the torsional stick-slip vibrations during drilling operations. The impact of various parameters such as the weight on the bit, rotational speed, and damping on the severity of vibration, in particular, stick-lip vibration, is analyzed. Various passive, active, and semi-active control strategies to mitigate the torsional vibrations have been studied and implemented with varying degrees of success, subject to continual development. From the simulation, the WOB, the drive torque, and rotational velocity determine the stick-slip onset and severity. This paper focuses on active control of the rotational speed and the weight on the bit by systematic adjustment to eliminate stick-slip while avoiding other undesirable effects and thus achieving optimum performance. Further study will be on multi-stability analysis to define the optimum operation zones and the design of vibration reduction tools and control strategies.