Study of a Viscoelastic PMMA String in a Damped Pendulum

The viscoelastic behavior of polymer optical fibers has garnered increasing interest due to their application as fiber sensors. A common technique for determining the storage and loss modulus of optical fibers involves fitting an exponential model to damped oscillatory motion. However, few studies address the challenge of identifying and specifying the various internal and external contributions to damping. The damping of a simple pendulum is influenced by several factors, such as the friction at the pivot and air drag on the string. In this case, the bob and the string are a coupled oscillating system, for its study, we used a bare polymethyl methacrylate optical fiber as a non-ideal, extensible, and viscoelastic string. The optical fiber was attached to a quasi-punctual support to minimize friction at the pivot. We considered the contribution to the damping of the pendulum due to air drag on the bob by varying the bob’s frontal area and extrapolating to the limit case where the frontal area of the bob tends to zero. This approach allowed us to calculate the damping coefficient solely due to the viscoelastic properties of the string. By conducting a dynamic analysis of the forces along the string and considering the interaction between the string and bob through the viscosity, we calculated the complex Young’s modulus, a key parameter in understanding the viscoelastic properties of the system.