Question

If the transfer function of a system is \( G(s) = \frac{A}{s^2 + \omega^2} \), then the steady state gain of the system to a unit step input is:

• A. \( \frac{A}{\omega^2} \)
• B. zero
• C. infinity
• D. Not possible to be determined

Hint:

Use Final Value Theorem: \( \lim_{t \to \infty} y(t) = \lim_{s \to 0} sY(s) \).

Answer 1

The Correct Option is A

The steady state value of the system’s output to a unit step input can be found using the Final Value Theorem: \[ \lim_{t \to \infty} y(t) = \lim_{s \to 0} s \cdot G(s) \cdot \frac{1}{s} = G(0) = \frac{A}{\omega^2} \]