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hello welcome back i now like to do a quick example illustrating how to apply the circle criterion so were going to consider this uh this system illustrated here um so weve got our truck that can slide from side to side and its connected to the wall uh by a spring and a damper were just going to assume that it obeys this differential equation here um so q double dot plus q dot plus q plus and this is going to be our nonlinear function h of q and we dont know what this is but were going to suppose that we know that it lies within a sector where the slopes of the line in the sector are two-thirds and one half so h of q is some nonlinear function that passes through the origin um so h of q is here we dont know what it is but the nonlinearity always lies within this sector here so were able to apply the circle criterion so in order to apply the circle criterion um to this system here the first thing we have to do is put it in our standard form of a linear system in feedback with a