P9.3 (a) Find a suitable contour s in the s -plane that can be used to determine whether all roots of the charac teristic

P9.3

(a) Find a suitable contour Γs in the s-plane that can be used to determine whether all roots of the charac

teristic equation have damping ratios greater than ζ1.

(b) Find a suitable contour Γs in the s-plane that can be used to determine whether all the roots of the char

acteristic equation have real parts less than s = −σ1.

(c) Using the contour of part

(b) and Cauchy’s the

orem, determine whether the following characteristic equation has roots with real parts less than s = −1:

q s( ) = + s s 3 2 11 + + 56s 96.