I am developing a concise yet rigorous treatment of forced oscillations, resonance and harmonic interactions in a simple electromechanical nonlinear system. The focus is on analytical techniques only; no numerical simulations are required at this stage. The work I need starts from the ground up: • write down a clear statement of the nonlinear governing equation that captures the essential electromechanical coupling; • highlight the small parameter(s) and show how near-resonant forcing enters; • carry out a multiple-scales expansion and derive the associated modulation equations; • analyse the resulting slow-flow for steady-state amplitudes, saturation behaviour, detuning effects and the role of multiple harmonics and higher-order system-forcing nonlinearities. Please organise the derivations so that each step is transparent and can be followed by someone familiar with dynamical-systems methods. A short explanatory note beside every major result will be appreciated. The deadline is flexible, but I would like the full mathematical formulation and analysis delivered as a clean, well-commented document (LaTeX).