Sketch the analogue of the trace-determinant plane in the bk-plane

Question Consider, The motion of a a damped harmonic oscillator is described by x′′ x ″ + bx′ b x ′ + kx=0 k x = 0, where b is greater than or equal to 0 A) Rewrite as a two dimensional linear system. x′=y x ′ = y y′ y ′ = - (by+kx) (b y + k x) B) Sketch the analogue of the trace-determinant plane in the bk-plane. That is, identify the regions in the relevant portion of the bk-plane where the corresponding system has similar phase portraits. I have cut out most of my answer etc as it seems to of merely confused people, how does one answer this question?