Drawing root locus for open loop transfer function

Question

1) Using Routh criterion find out stability of system whose characteristics equation is given as: S⁴+8S³+18S²+16S+5 =0

2) F(S) = S⁶+S⁵-2S⁴-3S³-7S²-4S¹-4=0. Determine the number of roots falling in RHS plane and LHS plane.

3) Design Nyquist plot for system whose open loop transfer function is G(S)H(S) =K/S (S+2) (S+10). Find out range of K for which closed loop system is stable.

4) Build Nyquist plot for feedback control system whose open loop transfer function is given: G(S)H(S) =5/ S(1-S). Explain the stability of open loop and closed loop transfer function.

5) Draw the Nyquist plot for system with open loop transfer function G(S)H(S)=K(1+0.5S) (1+S)/(1+10S) (S-1). Find out the range of values of K for which system is stable.

6) Draw root locus for open loop transfer function of unity feedback control system given below: G(S)H(S)=K/S(S+2)(S+4).

7) Draw root locus for open loop transfer function of unity feedback control system given below: G(S)H(S)=K/S(S+1)(S+2). Also determine K of breakaway point.