### Control Systems Objectives Part 02

**20 .** Laplace transform of 1 is **ππ¬.**

**21 .** The Laplace transform of a unity function is** ππ¬ .**

**22 .** Under thermal and electrical system analogy charge is considered analogous to **temperature.**

**23 . ** ** Viscous current coefficient-Reciprocal of resistance** is the analogous pair under current force analogy.

**24 .** The Laplace transform of sinκt isκππ+κπ.

**25 . ** Laplace transform of π‘nβ1<(πβ1) (n is positive integer) is**πππ§**

**26 . ** The Laplace transform of e-2t is**ππ+π**

**27 .** Laplace transform (used to switch a function from the time domain to the s-domain) method of solution is applicable to equations containing **none of the above.**

**28 .** When analogy between liquid level and electrical systems is drawn, voltage is considered as analogous to **head.**

**29 .** Under force-voltage analogy, viscous friction coefficient is analogous to **resistance.**

**30 .** The inverse Laplace transform of κπ (π 2+κ2) **is πκπ [cosκt-1]**

**31 . ** The system with characteristic equation s4+3s3+6s2+9s+12=0 **is unstable.**

**32. ** The characteristic equation s2+ 4s2+8s+12 represents a** stable system.**

**33 . ** The impulse responses of systems are given below.**sinκt **represents an unstable system.

**34 . ** A system with characteristic equation s3+14s2+56s+k=0 will be stable if0 0 and 784 β** K 14 > 0 **or 784 β K > 0 or K < 784 Therefore 0 < K < 784 is the required condition for the system to be stable.

**35 . ** The characteristic equation of a system is s4+3s3+6s2+9s+12=0 . in order to ensure that the system be stable, K must be greater than **zero a and less than 10.**

**36 . ** Fig. 20 represents the impulse response given by e-**tsin3t.**

**37 . ** If a zero appears in the first column of the Routh table, the system is **necessarily unstable.**

**38 . ** The roots of the characteristic equations of several systems are given below**.2,-1,-3** roots represents unstable system.

**39 . ** Which of the following characteristic equation represents a stable system **s2+7s2+7s+46.**

**40 . ** For the characteristic equation 2s3+4s2+4s+12=0 the number of roots with positive real parts is **two.**