<p>This study deals with an analytical study of the modal interactions during the planar vibration of a string with smooth curved obstacles at both ends. We briefly discuss the equations of motion and appropriate boundary conditions using the Lagrangian framework. The contact between the string and the obstacles at both ends varies with time, creating a moving boundary problem that has been converted into a fixed domain at the expense of nonlinearity. The first part of this investigation examines the dynamics of a string vibrating against obstacles of two different sizes. To articulate the effect of nonlinearities on the modal interactions, we use method of multiple scales (MMS) that provides the slow flow equations controlling the amplitude and phase. We use these equations to investigate the mode-locked periodic solutions as the fixed points of the evolution equations of a suitably defined relative phase in conjunction with the amplitude equations. A close investigation of these mode-locked solutions leads to the concept of equipartition of energy. Further, we find that the relative nominal curvature of the two obstacles is an important parameter that influences the vibration characteristics of the system. It is observed that when both obstacles are identical, modal interactions vanish completely up to the second order of MMS, which generates the need for more detailed analysis. Therefore, the second part briefly explores the potential scenarios involving similar obstacles. We compute the slow flow equations up to the third-order term to examine the effects of identical obstacles on the dynamics of the system. When there are similar obstacles on both sides, these slow flow equations have a different set of fixed points.</p>