s-plane stability concept

Ask

The constant damping loci $s= a+jb$ where 'a' represents the real part ideally indicates

(a) damping factor

(b) rate of decay time of the system response

(c) rate of rise time of the system response

(d)All the Above

Answer is ( d )

Concept

A pole in s-plane is given by $s= a+jb$ where 'a' is real part and 'b' is the imaginary part.Here, the real - part 'a' determines the  damping factor . This ideally indicates the rate of rise  or rate of decay of time response of the system

Large value of 'a' represents small time constant $\implies$ faster decay.
As can be seen from figure, the loci on left half of s-plane denotes positive damping
While , the loci on the right half of s-plane denotes negative damping .

Concept of s-plane : http://nptel.ac.in/courses/108103008/6