## 2 Background  
### Experiments in Structural Vibration Control  
Experiments with TLDs are particularly important in the field of structural vibration control for several reasons. First, the behavior of TLDs is typically modeled using fluid dynamics and vibration theory. Second, TLDs often exhibit nonlinear behavior due to fluid sloshing, which can be difficult to predict accurately using purely analytical methods. Experiments help identify and account for these nonlinearities, improving control strategies and damper design [14]. In addition, experimental studies allow engineers to optimize key parameters, such as the size, shape, and placement of TLDs, ensuring maximum vibration suppression for specific structures. These experiments help refine the design to achieve greater efficiency [15]. Furthermore, experiments replicate real-world conditions (such as wind, earthquakes, and other dynamic forces), helping to assess how TLDs perform under actual loading scenarios. This is critical for ensuring safety and stability in applications like tall buildings or bridges [16]. Testing new technologies, like the integration of MRFs in TLDs, requires experiments to validate how these innovations enhance performance, offering active or semi-active control of vibrations [17].  
[PERSON] et al. [18] proposed an experimental design to analyze the viscous damping coefficient in a mass/spring/damper system using different fluids such as water, edible oil, and motor oil. By observing the free decay of a mass submerged in the fluids, the logarithmic decrement of the response is measured, allowing for the determination of the damping coefficient. Their findings confirm that the damping coefficient increases with fluid viscosity, demonstrating a clear relationship between viscosity and energy dissipation. The inclusion of vegetable-based oil aims to evaluate its performance as an alternative to petroleum-derived lubricants due to its renewable nature and high biodegradability, which make it a promising option in sustainable engineering applications.  
To investigate the impact of magnetic fields on the fluid viscosity and, consequently, on its damping, a uniform and controlled magnetic field is required. The Helmholtz coil is a pair of identical coils placed symmetrically and separated by a distance equal to the radius of the coils. This specific arrangement, in which the current flows in the same direction on both coils, produces a nearly uniform magnetic field in the region between the coils, making them ideal for practical experimentation and analysis. This principle relies on the Biot-Savart law and the superposition of magnetic fields [19].  
The viscosity of ferromagnetic fluids varies with the strength and orientation of an applied magnetic field, depending on the ratio of hydrodynamic stress to magnetic stress [20]. For low ratios, viscosity is field-dependent, while at high field values, it becomes field-independent. [PERSON] et al. [21] devised a cylindrical container-tuned magnetic fluid damper and studied the effects of varying the depth of the magnetic fluid and the applied magnetic field on the damper's performance. It was found that the presence of magnetic fluid significantly suppresses vibrations, especially near the natural frequency of the structure.