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Let Y(s) be the unit-step response of a causal system having a transfer function G(s) = (3 - s)/((s + 1)(s + 3))
that is, Y(s) = G(s)/s. The forced response of the system is
- u(t) - 2e^(-t)u(t) + e^(-3t)u(t)
- 2u(t) - 2e^(-t)u(t) + e^(-3t)u(t)
- 2u(t)
- u(t)
Correct answer: u(t)
Solution
The forced (steady-state) response comes from the input pole at s=0, with coefficient G(0) = (3-0)/((0+1)(0+3)) = 3/3 = 1. So the forced response is 1*u(t) = u(t), not 2u(t).
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