-
By a suitable choice of the scalar parameter K, the system shown in the figure below, can be made to oscillate continuously at a frequency of—
-
- 1 rad/s
- 2 rad/s
- 4 rad/s
- 8 rad/s
- 1 rad/s
Correct Option: C
To make the system oscillatory the imaginary part in the C.E. equation of the given system must be zero. So first we calculate C.E.
Here,
| G(s) | |
| s(s + 2) (s + 8) |
H(s) = 1
1 + G(s) H(s) = 0 is the C.E.
or s
(s + 2) (s + 8) + K = 0
s (s2 + 10s + 16) + K = 0 (∴ s = jω)
jω(– ω2 + 10 jω + 16) + K = 0
– jω3 – 10ω2 + K = 0
– j(ω3 – 16ω) – 10ω2 + K = 0
Hence for system to be oscillatory
ω3 – 16ω = 0
ω2 – 16 = 0
or
ω = 4
