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Assertion (A): The steady state response, of a stable, linear, time invariant system, to sinusoidal input depends on initial conditions.
Reason (R): Frequency response, in steady state, is obtained by replacing s in the transfer function by jω
  • a)
    Both A and R are correct and R is correct explanation of A
  • b)
    Both A and R are correct but R is not correct explanation of A
  • c)
    A is correct but R is wrong
  • d)
    R is correct but A is wrong
Correct answer is option 'D'. Can you explain this answer?
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Assertion (A): The steady state response, of a stable, linear, time i...
Steady state response does not depend on initial conditions.
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Assertion (A): The steady state response, of a stable, linear, time i...
Steady State Response and Frequency Response

Steady State Response: The steady state response of a stable, linear, time invariant system to sinusoidal input depends on initial conditions. This means that the final output of the system after it has settled into a steady state will be affected by the initial conditions of the system.

Frequency Response: The frequency response of a system is the steady state response of the system to a sinusoidal input at different frequencies. It is obtained by replacing 's' in the transfer function by 'jω', where ω is the frequency of the input sinusoid.

Assertion and Reason

Assertion (A): The steady state response, of a stable, linear, time invariant system, to sinusoidal input depends on initial conditions.

Reason (R): Frequency response, in steady state, is obtained by replacing s in the transfer function by jω.

Option D is the correct answer, which means that Reason (R) is correct but Assertion (A) is wrong. This can be explained as follows:

- Reason (R) is correct: The frequency response of a system is obtained by replacing 's' in the transfer function by 'jω', which represents the frequency of the input sinusoid. In steady state, the output of the system will be the same as the input sinusoid, but with a different amplitude and phase shift. This is because the system will have a different response to different frequencies, which is captured by the frequency response.
- Assertion (A) is wrong: The steady state response of a system to a sinusoidal input does not depend on initial conditions. This is because the steady state response only considers the long-term behavior of the system, after it has settled into a stable state. The initial conditions only affect the transient response of the system, which is the behavior of the system before it reaches a steady state. Once the system has reached steady state, the initial conditions no longer matter.

Conclusion

The steady state response of a system to a sinusoidal input does not depend on initial conditions. The frequency response captures the steady state behavior of the system at different frequencies, and is obtained by replacing 's' in the transfer function by 'jω'.
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Assertion (A): The steady state response, of a stable, linear, time invariant system, to sinusoidal input depends on initial conditions. Reason (R): Frequency response, in steady state, is obtained by replacing s in the transfer function by jωa)Both A and R are correct and R is correct explanation of Ab)Both A and R are correct but R is not correct explanation of Ac)A is correct but R is wrongd)R is correct but A is wrongCorrect answer is option 'D'. Can you explain this answer?
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