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. 1/2`S^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 function`F(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