Solution Found!
Consider the following transfer function: Y(s) 5 G(s) =
Chapter 4, Problem 4.2(choose chapter or problem)
Consider the following transfer function: Y(s) 5 G(s) = U(s) = lOs + 1 (a) What is the steady-state gain? (b) What is the time constant? (c) If U(s) = 2/s, what is the value of the output y(t) when t~oo? (d) For the same U(s), 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, that is, the unit rectangular pulse, what is the output when t-oo? (t) If u(t) = S(t), that is, the unit impulse at t = 0, what is the output when t-oo? (g) If u(t) = 2 sin 3t, what is the value of the output when t-oo?
Questions & Answers
QUESTION:
Consider the following transfer function: Y(s) 5 G(s) = U(s) = lOs + 1 (a) What is the steady-state gain? (b) What is the time constant? (c) If U(s) = 2/s, what is the value of the output y(t) when t~oo? (d) For the same U(s), 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, that is, the unit rectangular pulse, what is the output when t-oo? (t) If u(t) = S(t), that is, the unit impulse at t = 0, what is the output when t-oo? (g) If u(t) = 2 sin 3t, what is the value of the output when t-oo?
ANSWER:Step 1 of 7
Given a transfer function of 1st order:
We can deduce the ODE with initial condition 
Then, knowing the ODE under study we can apply the definition of the Laplace Transform to obtain the output of the system 
