Consider the following transfer function:

G(s)= Y(s) / U(s) = 3e^−s / 10s + 1

(a) What is the steady-state gain?
(b) What is the time constant?
(c) If U(s) = 4/s, what is the value of the output y(t) when t → ∞?

(d) For the same input, what is the value of the output when t = 10? What is the output when expressed as a fraction of the new steady-state value?

(e) If U(s)=(1−e ^−s)/s, the unit rectangular pulse, what is the output when t → ∞?

(f) If u(t) = δ(t), the unit impulse at. t = 0, what is the output when t → ∞?

(g) If u(t) = 5 sin 2t, what is the value of the output when t → ∞?