Lyapuniv-functions

We have the system of ODEs

$y_1'= y_2$

$y_2'=-y_2-\sin(y_1)$.

Decide for each of the following functions whether it is a Lyapunov-function of $(0,0)$ or not:

$V(y_1,y_2)= y_1^2+y_2^2$.

$V(y_1,y_2)= \frac{y_2^2}{2}+(1- \cos(y_1))$.

$V(y_1,y_2)= \frac{(y_1+y_2)^2}{2} + y_1^2 + \frac{y_2^2}{2}$.

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Mathe Mathe
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