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I'm doing a project in which i'm attempting to model the motion of a wing using a system of second order differential equations. This is a 2-degree-of-freedom model based on the quantities pitch, a(t), and plunge, h(t). I know what pitch is, but what is plunge? and why is it affected by pitch? Where do these equations come from?

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This looks like a flutter system of a representative wing section. Plunge is the vertical degree of freedom as shown in the diagram below (the other degree of freedom is pitch, $\theta$ or $\alpha$ in your assignment). You also have structural damping terms, which are omitted in the diagram.

Aeroelastic representative section

Image ref: https://www.researchgate.net/figure/Sketch-of-airfoil-aeroelastic-system_fig1_313820106

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