Question

Consider the transfer function: G(s) = 8/(s² + 4s + 8). If the input is a step response u(t), what is the steady-state response as t → [infinity]? Solve this using.

Answer 1

The steady-state response of the system is 1 as t → ∞.

Step-by-step explanation:

The steady-state response of a system can be found by evaluating the transfer function at s = 0. To do this, we substitute s = 0 into the transfer function G(s) = 8/(s² + 4s + 8):

G(0) = 8/(0² + 4(0) + 8) = 8/8 = 1

Therefore, the steady-state response as t → ∞ is 1. This means that the output of the system will reach a constant value of 1 as time goes on.