#### Instrumentation and Process Control

1

For the time domain function f(t) = t, the Laplace transform of int_0^t  f(t)dt is given by

A. 1/2S^3
B. 2/S^3
C. 1/S^3
D. 2/S^2

2

What is the Laplace transform of sin t ?

A. (1)/(S^2 + 1)
B. (S)/(1 + S^2)
C. (1)/(S^2 - 1)
D. (S)/(S^2 - 1)

3

The root locus plot of the roots of the characteristics equation of a closed loop system having the open loop transfer function (K(S+1))/(2(2S+1)(3S+1)) will have a definite num-ber of loci for variation of K from 0 to oo. The number of loci is

A. 1
B. 3
C. 4
D. 2

4

A control system has the following transfer functionF(S) = ((S-1)(S+1))/(S(S-2)(S+4))

The initial value of the corresponding time function is

A. 1
B. 1/8
C. 7/8
D. - 1

5

Find the ultimate gain and frequency for a proportional controller in the case of a process having the transfer function Gp(s) = 1/(4s + 1)(2s + 1)(s + 1).

A. W = 1//sqrt(14),K_C= 45//7 sqrt(14)
B. W = sqrt(7//6),K_C= 46/3
C. W = 1, K_C = 13
D. W = sqrt(7//8),K _C = 45/4