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Our thin films are constituted by Permalloy nanoparticles the type: (Ni81Fe19)1-x(Al2O3)x and Employing Radiofrequency Sputtering, they are deposited on Corning glass substrates in a dynamic field along the hard axis of magnetization, the samples were subjected to a magnetic field applied in their plane. We utilized the ranges of argon pressures of 4.10-3 and 60.10-3 (mbar). The rates of Al2O3 substitution are set at 24, 34 and 44% at. The measurements and damping coefficient deduced from this adjustment align with the calculations of permeability spectra obtained from the Gilbert Lifshitz Landau model. After this adjustment, the damping ratio values accord with the values from the previous research. Similar to pressure, the damping coefficient increases linearly with pressure. A linear relationship exists between the coefficient of depth and the Full Width at Half-Maximum (FWHM) values of the imaginary part of the permeability dependent frequency. The actual fits were done through the convolution of a Gaussian line width for the inhomogeneity term and a Lorentzian line width for the TMS and a magnon-electron (m-e) terms. Based on broadband ferromagnetic resonance measurements of the Permalloy films, the saturation magnetization field (4Ms) increase as Ha grew and remained close to the theoretical value. This work helps us understand to the physical origin of the Gilbert damping in magnetic films and utilized in spintronic devices and the sensors applications.