I'm working in the following paragraph
If I consider a model which is supported to rotate freely about an axis through its center of gravity. if the model is placed in a uniform flow perpendicular to the axis, then it does pitching motion. Let $\alpha$ the angle of attack of the model of time t'. Then the pitching motion is described $$\frac{d^{2}}{dt'}\alpha=\frac{M}{I}.$$ Where M is a moment of aeorodnamic force acting acting of the model and I is the moment of inertia of the model. An experiment shows that the moment M is a single-valued funciton of $\alpha$ and $\frac{d}{dt'}\alpha$. Accordongly, the moment M has a period $2\pi$ in $\alpha$. Furthermore, if the model has fore-aft and up-down symmetries, the moment M has period $\pi$ in $\alpha$ and is odd function with respec to $(\alpha, \frac{d}{dt'}\alpha)$. There fore if we take only the main terms which describe the motion, we have $$\frac{d^{2}}{dt}x +\sin x + (\varepsilon_{1}+\varepsilon_{2} \cos x)\frac{d}{dt}x=0.$$ Where $\varepsilon_{1},\varepsilon_{2} $ are small constants.
Due my poor knowledge in physics I don't understand how get $\frac{d^{2}}{dt}x +\sin x + (\varepsilon_{1}+\varepsilon_{2} \cos x)\frac{d}{dt}x=0 $. Thanks in advance!
More precisely I'm reading 