EAS 340: Quiz 3
Name
Draw the root locus plot for positive K, including labeling your axes(!), and answer the following questions for the
system
( 1)( + 4 + i)( + 4 i) + K = 0
Write your final answer on the lines provided!
Solution: For convenience in som

MAE 340: Test 1
Name:
Problem 1: For the LTI ODE
5
x(t) + 15x(t)
+ 125x(t) = 0
,
x(0) = 4 ,
x(0)
=2
1a: (20 points) Solution: The Characteristic Equation and its roots are used to fill in the blanks below:
52 + 15 + 125 = 0 = 2 + 3 + 25 = 2 + 2n + n2
3

MAE 340: Homework 11
Particular Solutions
1. Find the particular solution for the following systems:
(a)
x
(t) + 2x(t)
+ 10x(t) = f (t)
,
f (t) = 4
Solution: The forcing is a constant, so the form of the particular solution is xp (t) = C. Substituting,

MAE 340: Test 1
Name:
Problem 1: For the LTI ODE
5
x(t) + 12x(t)
+ 80x(t) = 0
,
x(0) = 4 ,
x(0)
=2
Solution: The Characteristic Equation and its roots are used to fill in the blanks below:
52 + 12 + 80 = 0 = 2 + 2.4 + 16 = 2 + 2n + n2
2.4
1,2 = 1.2 i3.8

MAE 340
Homework 14
Solution
The following is based on the two-cart system shown in the notes on Multiple LTI ODE systems
1. Write a state-space model for the following system:
x
1 + 2(x 1 x 2 ) + 20(x1 x2 ) + x 1 + 10x1 = 0
2
x2 + 2(x 2 x 1 ) + 20(x2 x1

EAS 340: Quiz 4 Solution
Name
Find the complete solution x(t) and plot it to twice the settling time. For full credit, you must clearly label your
axes including numerical values, and sketch a reasonably accurate plot.
x
(t) + 2x(t)
+ 2x(t) = 4
, x(0) =

MAE 340: Quiz
Name:
For the homogeneous LTI ODE
2
d2 x
dx
d3 x
+
14
+K
+ Cx(t) = 0
3
2
dt
dt
dt
a) use Routh-Hurwitz to determine conditions for the values of K and C (if any) for which the system is stable
b) use Routh-Hurwitz along with axis-shifting to

MAE 340: Homework 9
Name:
1. For each of the following systems, find the complete solution and plot it out to two times the settling time, and
confirm that the complete solution settles onto the particular solution.
(a)
d2 x
dx
d3 x
+
3
+7
+ 5x(t) = 1
3
2

MAE 340: Homework 16
For each of the following systems,
a) find the frequency response function (FRF) as a function of
b) find the magnitude of the FRF as a function of
c) find the phase of the FRF as a function of
d) using your results from (2) and (3

MAE 340 Quiz 5
Name:
Write a state-space model for the system:
x
1 (t) 3 x 1 (t) x 2 (t) 18 x1 (t) x2 (t)] 4x 1 (t) 20x1 (t) = 3 + 4sin(2t)
x
2 (t) + 3 x 1 (t) x 2 (t) + 18 x1 (t) x2 (t)] = 8sin(2t) 15
The two inputs are u1 (t) = 1 , u2 (t) = sin(2t) and

MAE 340: Test 1
Name:
Problem 1: For the LTI ODE
5
x(t) + 9x(t)
+ 45x(t) = 0
,
x(0) = 4
,
x(0)
=2
Solution: The Characteristic Equation and its roots are used to fill in the blanks below:
52 + 9 + 45 = 0 = 2 + 1.8 + 9 = 2 + 2n + n2
1.8
1,2 = 0.9 i2.86 ,

MAE 340: Homework 15
1. For each of the following systems, find all transfer functions by using your own algebra, and then find their
poles and zeros:
a) x(t)
+ 2x(t) = 3u(t) ; the output is y(t) = 2x(t)
Solution: Take the Laplace transform of the LTI O

MAE 340: Homework 14
Name:
1. For each of the following three systems, find the complete solution and plot it out to two times the settling
time, as follows:
(a) Create a state-space model in MATLAB
(b) Use initial to find the response to the initial cond

MAE 340: Homework 12
Conversion to State Space
Find a state space model for each of the following systems. Use a separate input function for each independent
function of time on the RHS of the original equation.
1.
.
x (t) + x
(t) + 2x(t)
+ 10x(t) = f (t