Homework Assignment 4, Spring 2013
MechE 24352 Dynamic Systems and Controls
Due on February 20, 2013
Question 1.
Explain the concept of time constant by considering the EOM cx + kx = 0 with the initial dis
placement x(0) = x0 .
Question 2.
Rigid Massless

Homework Assignment 7, Spring 2013
MechE 24352 Dynamic Systems and Controls
Due on March 27, 2013
Question 1.
For the following system,
Derive the equation of motion (with the small angle assumption, and considering the horizontal position as the equilib

Homework Assignment 2, Spring 2013
MechE 24352 Dynamic Systems and Controls
Due on Jan 30, 2013
Question 1.
Find the inverse Laplace transforms of the following functions:
+5 a.) F1 (s) =
+5 b.) F2 (s) =
3s + 7
2s2 + 8s + 6
s3 40s2 + 17s + 370
s4 29s2 + 1

Homework Assignment 9, Spring 2013
MechE 24352 Dynamic Systems and Controls
Due on April 8, 2013
Question 1.
Consider the following state space system:
q1
q2
=
0
1
5 6
y1
y2
=
23
q1
+
q2
40
41
2 2
u1
u2
q1
q2
i.) Calculate the state transition matrix (t )

Homework Assignment 10, Spring 2013
MechE 24352 Dynamic Systems and Controls
Due on April 26, 2013
Question 1.
For the system shown in the gure above, obtain the overall transfer function G(s) = C(s)/R(s).
Question 2.
For each of the systems whose EOMs ar

Homework Assignment 11, Spring 2013
MechE 24352 Dynamic Systems and Controls
Due on May 10, 2013
Question 1.
Shown in the gure above is a system consisting of two pendulums, each consisting of a massless
rod of length L = 1.5m, and a bob of negligible rad

Homework Assignment 9, Spring 2013
MechE 24352 Dynamic Systems and Controls
Due on April 8, 2013
Question 1.
Consider the following state space system:
q1
q2
=
0
1
5 6
y1
y2
=
23
q1
+
q2
40
41
2 2
u1
u2
q1
q2
i.) Calculate the state transition matrix (t )

Homework Assignment 5, Spring 2013
MechE 24352 Dynamic Systems and Controls
Due on February 27, 2013
Question 1.
In the system shown above, the pulley has a mass M, radius R, and moment of inertia J about
its axis. The rope wound around the pulley is mass

Name: Andrew ID:
Question D-1 (10 points)
For a system Whose state spacggrcidel is give? begow, compute the transfer
a, a '
matrix [G(s)]: . W re *3
(3:) = Us 32] (3:) + [i 3] (:9
<i:)=[é 31] (3:) <1)
m 3 [2(3~22}+"1C§>+~C2 3022.) + 0&5? I)
v

Homework Assignment 8, Spring 2013
MechE 24352 Dynamic Systems and Controls
Due on April 3, 2013
Question 1.
Shown in the gure above is a system consisting of two pendulums, each consisting of a massless rod of length L = 1.5m, and a bob of negligible rad

Homework Assignment 3, Spring 2013
MechE 24352 Dynamic Systems and Controls
Due on Feb 6, 2013
Note: Homework problems where it is not explicitly instructed to use MATLAB or other software
should be done by hand, clearly showing all steps. You can of cour

Homework Assignment 8, Spring 2013
MechE 24352 Dynamic Systems and Controls
Due on April 3, 2013
Question 1.
Shown in the gure above is a system consisting of two pendulums, each consisting of a massless rod of length L = 1.5m, and a bob of negligible rad

Homework Assignment 7, Spring 2013
MechE 24352 Dynamic Systems and Controls
Due on March 27, 2013
Question 1.
For the following system,
Derive the equation of motion (with the small angle assumption, and considering the horizontal position as the equilib

Homework Assignment 1, Spring 2013
MechE 24352 Dynamic Systems and Controls
Due on Jan 23, 2013
Question 1.
Given z = 1 + 2 j and q = 3 + 4 j, calculate the following. Write the real part, imaginary part, magnitude and angle of each result. Write the resu

Homework Assignment 10, Spring 2013
MechE 24352 Dynamic Systems and Controls
Due on April 26, 2013
Question 1.
For the system shown in the gure above, obtain the overall transfer function G(s) = C(s)/R(s).
Question 2.
For each of the systems whose EOMs ar

Homework Assignment 1, Spring 2013
MechE 24352 Dynamic Systems and Controls
Due on Jan 23, 2013
Question 1.
Given z = 1 + 2 j and q = 3 + 4 j, calculate the following. Write the real part, imaginary part, magnitude and angle of each result. Write the resu

Homework Assignment 2, Spring 2013
MechE 24352 Dynamic Systems and Controls
Due on Jan 30, 2013
Question 1.
Find the inverse Laplace transforms of the following functions:
a.) F1 (s) =
b.) F2 (s) =
3s + 7
2s2 + 8s + 6
s3 40s2 + 17s + 370
s4 29s2 + 100
c.)

Homework Assignment 3, Spring 2013
MechE 24352 Dynamic Systems and Controls
Due on Feb 6, 2013
Note: Homework problems where it is not explicitly instructed to use MATLAB or other software
should be done by hand, clearly showing all steps. You can of cour

+2 for wn,
+2 for T,
+3 for plot
+3
Question 3.
+20
k
J
m
Derive the EOM of the above system. There is no slip between the pulley and the wire. Assume
initial displacement and velocity of the mass (downward) to be x0 and v0 , respectively. [Hint: When
the

Homework Assignment 6, Spring 2013
MechE 24352 Dynamic Systems and Controls
Due on March 4, 2013
Question 1.
Shown in the gure above is the block and pulley system you studied in HW5, Problem 1. The
pulley has a mass M, radius R, and moment of inertia J a

Homework Assignment 6, Spring 2013
MechE 24352 Dynamic Systems and Controls
Due on March 4, 2013
Question 1.
Shown in the gure above is the block and pulley system you studied in HW5, Problem 1. The
pulley has a mass M, radius R, and moment of inertia J a

Homework Assignment 5, Spring 2013
MechE 24352 Dynamic Systems and Controls
Due on February 27, 2013
Question 1.
In the system shown above, the pulley has a mass M, radius R, and moment of inertia J about
its axis. The rope wound around the pulley is mass