The paper "Inspection of Some Extremely Nonlinear Oscillators Using an Inventive Approach" by Galal M. Moatimid, T. S. Amer, and A. A. Galal introduces a novel technique to analyze highly nonlinear oscillators, which are challenging to study using traditional methods. The main objective is to apply the generalized He’s frequency formula (HFF) to provide analytical solutions for specific types of extremely nonlinear oscillators. This approach, referred to as the non-perturbative approach (NPA), converts nonlinear ordinary differential equations (ODEs) into linear ones, simplifying the analysis. The NPA is compared to conventional perturbation methods, which often rely on Taylor expansions to reduce problem complexity. The NPA, however, does not suffer from these limitations and can handle more complex nonlinearities. The method produces a new frequency similar to that of a linear ODE, leading to strong agreement with numerical findings and superior accuracy compared to other approximate methodologies. The theoretical findings are validated through numerical analysis using Mathematica Software (MS), demonstrating remarkable congruity between the numerical solution (NS) and the theoretical responses. The NPA also enables stability analysis, a capability not available with conventional methods. The paper concludes that the NPA is a valuable resource for analyzing oscillators with significant nonlinearity, offering exceptional versatility in addressing various nonlinear problems. Its applications in engineering and applied science highlight its importance in understanding and managing complex systems. Keywords: Nonlinear vibrations, Non-perturbative approach, He’s frequency formula, Stability diagrams, Numerical solutions, Tapered beam.The paper "Inspection of Some Extremely Nonlinear Oscillators Using an Inventive Approach" by Galal M. Moatimid, T. S. Amer, and A. A. Galal introduces a novel technique to analyze highly nonlinear oscillators, which are challenging to study using traditional methods. The main objective is to apply the generalized He’s frequency formula (HFF) to provide analytical solutions for specific types of extremely nonlinear oscillators. This approach, referred to as the non-perturbative approach (NPA), converts nonlinear ordinary differential equations (ODEs) into linear ones, simplifying the analysis. The NPA is compared to conventional perturbation methods, which often rely on Taylor expansions to reduce problem complexity. The NPA, however, does not suffer from these limitations and can handle more complex nonlinearities. The method produces a new frequency similar to that of a linear ODE, leading to strong agreement with numerical findings and superior accuracy compared to other approximate methodologies. The theoretical findings are validated through numerical analysis using Mathematica Software (MS), demonstrating remarkable congruity between the numerical solution (NS) and the theoretical responses. The NPA also enables stability analysis, a capability not available with conventional methods. The paper concludes that the NPA is a valuable resource for analyzing oscillators with significant nonlinearity, offering exceptional versatility in addressing various nonlinear problems. Its applications in engineering and applied science highlight its importance in understanding and managing complex systems. Keywords: Nonlinear vibrations, Non-perturbative approach, He’s frequency formula, Stability diagrams, Numerical solutions, Tapered beam.