## 4 Analysis of Results  
### Factors Affecting the Viscosity of the Magnetic Fluid  
In the first set of trials, elapsed times \(\Delta t\) of Sphere 1 between the two marks through the magnetic fluid without activating the magnetic field were measured. The statistics of the measurements are displayed in Table 2. The ambient temperature was kept between 23.4 and 23.7 \({}^{\circ}\)C during the test. [PERSON]'s correlation between the ambient temperature and the elapsed times was examined to assess whether the temperature affected the motion of the sphere. The correlation coefficient was \(-\)0.029, and the corresponding \(p\)-value was 0.936, indicating that the null hypothesis that considers that the temperature did not significantly affect the motion is true. Similarly, [PERSON]'s correlation between the relative humidity and the elapsed times was studied to assess whether the humidity affected the motion of the sphere. The correlation coefficient was \(-\)0.075, and the associated \(p\)-value was 0.838, indicating that the null hypothesis that the relative humidity did not significantly affect the  
Figure 9: Screenshot of Tracker software registering the motion of a sphere. motion of the sphere is true, which allows completely ruling out the influence of humidity on the motion of the sphere. In the second set of trials, elapsed times \(\Delta t\) of Sphere 1 between the two marks through the magnetic fluid with an active magnetic field were measured. The statistics of such measurements are shown in Table 3. The ambient temperature varied between 26.6 and 26.7 \({}^{\circ}\)C during the test. [PERSON]'s correlation between the ambient temperature and the elapsed times was examined to verify whether the temperature affected the motion of the sphere. The correlation coefficient in this case was 0.053, and the corresponding \(p\)-value was 0.910, showing that the temperature did not significantly affect the motion of the sphere. Next, [PERSON]'s correlation between the relative humidity and the elapsed times was studied to evaluate whether the temperature affected the motion of the sphere. In this particular case, the relative humidity remained constant, so it is not possible to determine if an association exists. To verify the effect of the magnetic field on the motion of the sphere through the magnetic fluid, a \(t\)-test for non-paired samples was performed to check the null hypothesis that the samples come from the same two underlying populations and have the same mean value. If a two-sample equal variance is considered (i.e., homoscedastic), the test returned the \(p\)-value 0.0109. If a two-sample unequal variance (i.e., heteroscedastic), the test returned the \(p\)-value 0.0260. In both cases, the null hypothesis can be rejected at the 95% confidence level. This result indicates that the magnetic field effectively increases the viscosity of the fluid and may allow the design of devices for active vibration control and TLDs. Additionally, the viscosity of the magnetic fluid has been evaluated in Equation (12), considering that the terminal velocity was reached in the tests. The mean dynamic viscosity of the fluid results in 70.4 kg/s/m for the off-state and increases to a mean dynamic viscosity equal to 78.1 kg/s/m when the magnetic field is activated. The results indicate that the viscosity of the fluid underwent significant modification under the influence of the magnetic field. However, the increased variability in the sample suggests a lack of satisfactory control over the viscosity of the fluid when the magnetic field is applied. This may be due to the trajectory of the sphere deviating slightly from the central axis of the tube rather than following an exact axial path from the outset. The random nature of the variance in the measurements is not to be discounted, and it is important