  This study investigates the nonlinear normal modes (NNMs) of a system
comprising of two coupled Duffing oscillators, with one oscillator being
grounded and with the coupling being both linear and nonlinear. The study
utilizes the eigenfunctions of the Koopman operator and validates their
connection with the Shaw-Piere invariant manifold framework for NNMs.
Furthermore, the study delves into the impact of internal resonance and
dissipation on the accuracy of this framework by defining a continuous
quantitative measure for internal resonance. The applicability and robustness
of the framework for the systems which are very similar qualitatively to that
of an ENO, are also observed and discussed about the limitations of the
approximation technique.
