Mary Cartwright studied analysis and nonlinear ordinary differential equations. With John Edensor Littlewood, she investigated forced oscillators of the Van der Pol equation type, where state-dependent damping and external periodic forcing interact.[ref]
On Non-Linear Differential Equations of the Second Order, Part I by Mary Cartwright and John Edensor Littlewood. Original 1945 byline and equation in the title
The motivation included radio engineering: a nonlinear oscillator need not respond like a linear resonator. Studying its long-term solutions requires understanding the dynamics over repeated forcing cycles, not just solving one instantaneous balance. Cartwright's own historical account describes this exchange between an engineering question and qualitative mathematics.[ref]
https://www.cambridge.org/core/journals/mathematical-gazette/article/abs/nonlinear-vibrations-a-chapter-in-mathematical-history/E9D6261C511996F950C0C4A961E0641F. Cartwright's own historical account of nonlinear vibrations
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