The vibration of a drill string is a key topic of study in drilling and mining engineering. Excessive Drill String (DS) vibrations can lead to early failure of bits due to fatigue, Drill Pipe (DP) fractures, bearing damage, and a decrease in the Rate of Penetration (ROP). This occurs when the drill string rotates at its natural frequency, which is known as resonance. A modal and harmonic vibrational analysis of a drill string up to 60-65 meters long was conducted in a vertical water well through parametric studies. This project investigates the vibration of a drill string under various parameters, including drill string lengths, Weight on Bit (WOB), and drill string rotational speeds. The Rotational Speed (RS) in the drill string induces lateral vibrations and stick-slip in torsional vibrations. Finite element modeling of the drill string was performed using ANSYS Workbench (Mechanical). Modal and harmonic frequencies were determined to obtain the optimal drill string length and rotational speeds, using Campbell diagrams and varying weights on bits. Different weights on the bit were assumed to simulate the drilling environment. One of the modern methods used to simulate dynamic behavior in drilling operations is random vibrational analysis. A random vibrational analysis of the drill string was performed in a vertical water well using ANSYS Workbench 2020. This analysis aimed to identify the frequency response of the drill string, with the probability of deformation for each sigma under random vibration being evaluated. The analysis indicated a higher probability approximately 99.7% of failure along the axis of the supplied PSD acceleration. The response power spectral density (RPSD) was analyzed in the x, y, and z directions, focusing on any point in the bottom hole assembly, primarily the bit. The response PSD results indicated that as the Drill Pipe (DP) increased, resonance spikes rose across all axes, leading to lateral and longitudinal vibrations in the drill string. These findings highlight lateral movement as a primary cause of vibration, offering insights for optimizing drilling parameters.