### Control Systems Objectives Part 03

**41 .** The roots of the characteristic equations of several systems are given below. All of these represents unstable systems EXCEPT-**1, +1.**

**42 . ** For what values of K does the polynomial s3+(4+4k)s2+6s+12 have roots with negative real parts **k>-2.**

**43 .** The characteristic equation s3+8s2+14s+24=0 represents a **stable system.****Question 44 to 47 refer to data given below:**

Let us consider the second order system

2 d2yππ‘2 + 4 πyππ‘ + 8y = 8x.

**44 . ** The damping ratio is **0.5.**

**45 . ** The undamped natural frequency is **0.1.**

**46 .** The damping coefficient is **1.**

**47 . ** The time constant is **1.**

**48 .** For what range of values of K the system having characteristic equation s2+Ks+2K-1=0 will be stable?** K>ππ**

**49 . ** For the given signal flow graph, πΆπ
is **unity.**

**50 . ** When all the coefficients of the characteristic equation do not have the same sign, the system is **unstable.**

**51 .** The roots of the characteristic equations of several systems are given below. Which of these sets presents marginally stable systems? –**2+j, -2-j, 2j, -2j.**

**52 . ** The transfer function of a system is given by

κ=1π (π +2+4j)(s+2β4j)The number of poles is **three.**

**53 .** If any coefficient of the characteristic equation of a system are zero, the system is **unstable.**

**54 .** A system has poles at -1, -5 and zeros at 1 and -2. The systems is **stable.**

**55 . ** The open loop transfer functions of systems are given below. Identify the system that is not stable for all values of gain constant K.κ**=π(π¬+π)π(π+ππ£)(βπ¬+π)**

**56 . ** The number of roots with positive real parts for the polynomial s3+s2-s+1 is **two.**

**57 . ** A system having characteristic equation (s+1) (s+2) (s-3) is** unstable.**

**58 . ** The Laplace transform of circuit I(t) is given by

i(s)=**π(π¬)πΉπ³+π**

**59 .** The number of roots with positive real parts for the polynomial s4+2s3+2s2+2s+1 is **none.**

**60 . ** The differential equation of an integer is dyππ‘=x. The integer is **marginally stable.**