ECE 317 Homework 1 Answers
1) List the 3 steps shown in class to solve an ordinary differential equation using Laplace
transforms.
a. Laplace transform
b. Partial Fraction Expansion
c. Inverse Laplace transform
2) What is the response, or output, of a system G(s) = 1
𝑠+10 to a unit impulse at the input?
r(t) = δ(t)
Y(s) = R(s) * G(s) = 1 * 1
𝑠+10 = 1
𝑠+10
L-1 {Y(s)} = e-10t = y(t)
*I would accept Y(s) or y(t) as an answer here, but know how to do both though!
3) What would be the DC gain of the system in question 2?
At DC, s = 0, therefore gain of system, G(0) = 1
10
4) Can we use the final value theorem to solve for the system G(s) = 7
𝑠2+4? Why or why not?
No, to use final value theorem, all poles of s*F(s) must be in the open left half plane, with
one simple pole possible at the origin.
Roots of the denominator are the pole locations: (s2+4) = -2i,+2i
5) Find the initial value of the system in question 4.
lim
s−>∞ sF(s) = 7𝑠
𝑠2+4 = ∞
∞ = 7
2𝑠 = 0
*using L’Hopital’s rule
6) The output response of a system has 2 components. What are they?
a. Transient
b. Steady state