Being G(s)= -K(s+1)²/s²+2s+2 and K>0 I need a) K value for stability on a closed loop b)sketch the root locus c) the position of the poles on a closed loop for K=1 and for K=2 I have no ideia on how to solve this

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.