Correct Answer - Option 2 :
\(\frac{1}{2}\) rad/s
Concept:
The output response of a system is equal to the sum of natural response and forced response.
Forced response: The response generated due to the pole of the input function is called the forced response.
Natural response: The response generated due to the pole of system function is called the natural response.
Analysis:
\(Y(s) = \frac{1}{s}-\frac{3}{s+1}+\frac{3}{s+2}\)
The forced response = 1/s
The forced response will be 2 at 0.5 rad/sec
The forced response = 1/0.5 = 2.