What exactly is "plunge?"
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.



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