### 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 d2y𝑑𝑡2 + 4 𝑑y𝑑𝑡 + 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>𝟏𝟐

49 . For the given signal flow graph, 𝐶𝑅 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
Ꝋ=1𝑠(𝑠+2+4j)(s+2−4j)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.Ꝋ=𝐊(𝐬+𝟏)𝒔(𝒔+𝟐𝐣)(−𝐬+𝟒)

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)=𝐕(𝐬)𝑹𝑳+𝟏

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 dy𝑑𝑡=x. The integer is marginally stable.