6. (15pts) Given the feedback system shown below, RO-Σ 5 s(s+2) 1 + as (a) (8pts) Put the characteristic equation in Roo-Locus form with respect to the parameter a and identify the corresponding loop transfer function L(s). (a) (7pts) Sketch the root locus diagram with respect to the parameter a as it varies from 0 to 0.

Fig: 1