The attachment oscillator, a crucial system in nanophysics and nanotechnology, plays an essential role in nano/micro-electromechanical systems, molecular devices, and the formation of nanofiber membranes. Traditional analytical approaches to deducing the amplitude-frequency relationship (AFR) for such oscillators, including energy balance theory (EBT) and homotopy perturbation methods (HPM), often show limitations in predicting frequency behavior while comparing with the numerical results. This paper presents an analytical solution derived using the energy balance method, which provides a more accurate AFR for low-amplitude oscillations than existing models. Our result shows excellent agreement with numerical simulations, while other contemporary approaches exhibit significant deviations. This advancement offers a more robust understanding of attachment oscillators and their applications in nanotechnology, providing a new analytical framework that surpasses previous works.