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The unit step response y(t) of a linear system is

y(t) = (1 – 3e-t + 3e-2t) u(t)

For the system function, the frequency at which the forced response becomes 2 is

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  1. \(\frac{1}{\sqrt{2}}\) rad/s
  2. \(\frac{1}{2}\) rad/s
  3. \(\sqrt{2}\) rad/s
  4. 2 rad/s

Answer (Detailed Solution Below)

Option 2 : \(\frac{1}{2}\) rad/s
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Detailed Solution

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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. 

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