He's frequency-amplitude formulation for nonlinear oscillators using Jacobi elliptic functions

In this work, the Duffing's type analytical frequency-amplitude relationship for nonlinear oscillators is derived by using Hes formulation and Jacobi elliptic functions. Comparison of the numerical results obtained from the derived analytical expression using Jacobi elliptic functions with respect to the exact ones is performed by considering weak and strong Duffing's nonlinear oscillators.