This paper provides an overview of the application of Digital Twins (DTs) for mechanical vibration systems. DT revolutionized various fields such as aeronautics, industry, and civil engineering. Combining this technology with mechanical vibration makes it a powerful tool. We proposed an architecture for implementing a digital twin for a mechanical vibration system. The framework includes the creation of a virtual model, data processing to ensure the transfer of data without noise from the physical model to the virtual model, and real-time communication using Internet of Things (IoT) sensors. To validate the proposed architecture, an application was developed for a cantilever beam based on the finite element method and the Euler-Bernoulli method for this kind of beam. The study highlighted the importance of DTs for predictive maintenance and extending the life cycle of the mechanical systems. Finally, the paper discusses the key challenges encountered in implementing DTs, like the integration issues, the need for qualified personnel, and cybersecurity threats.