ME 3015 HW Set #3 Solution
Problem 1.
a)
By performing a Free-Body-Diagram analysis on the block and assuming x2 > x1,
m1 2kx1 k ( x2 x1 ) u 3kx1 kx2 u (1)
x
Similarly, at the node associated with x2,
mnode2 (0) 2 0 k ( x2 x1 ) bx2
x
x
Which then can be r
ME3015 PROBLEM SET #2 (25 points). Document as outlined in the course admin letter.
SOLUTIONS
1. (5 points) Solve the following differential equation of motion using Laplace Transform
Techniques:
4 x 0 x(0) 5, x(0) 0
x
s X (s) sx(0) x(0) 4 X (s) 0
2
Subs
ME3015 PROBLEM SET #1 (25 points).
SOLUTION
1.
(a) Find the inverse Laplace transform for:
F ( s)
s 2 6s 2
s( s 1) 2
[Sol] Partial fractional expansion:
F ( s)
2
1
3
s s 1 ( s 1) 2
f (t ) 2 1(t ) et 3te t (ANS)
(b) Obtain f (0) and f () . Use the initia
George W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology
ME3015A
HW SET #6 Solutions
_
B-10-6
B-10-8
B-10-10
B-10-11
B-10-12
.
B-10-13
HOMEWORK SET 7
ME3015
B-10-15
CONTINUED ON NEXT PAGE
B-10-15 CONTINUED
B-10-17
B-10-17 CONTINUED AT NEXT PAGE
B-10-17 CONTINUED
B-10-18
B-10-20
PROBLEM B-10-20 CONTINUED AT NEXT PAGE
B-10-20 CONTINUEDROOT LOCUS PLOT ON NEXT PAGE
George W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology
ME3015
HW SET #8
Complete by 7/29/2005
_
1)
2)
3)
4)
Text Problem B-9-1.
Text Problem B-9-2.
Text Problem B-9-6.
Text Problem B-9-15.
George W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology
ME3015 Midterm Solutions
Summer 2005
NAME_Key_
_
Problem
Points
I
II
/25
Total
/25
/50
Please read this first:
1. The test is closed-book and closed notes. A Laplace Trans
G.W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology
ME3015
Computer Assignment I
Due: Friday 6/24/2005
_
The computer assignment below may be done by teams of up to 2 students/team. Each
group is required to submit one report wi
George W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology
ME3015A
Computer Assignment II
Due 7/22/2003
_
This assignment may be done by groups of at most two (2) students per group.
A simplified schematic diagram of model of a ve
George W. Woodruff School of Mechanical Engineering
ME3015A
Quiz #1
Summer 2005
NAME _Key_
_
1) Indicate whether the following input-output relationships are Dynamic (D) or Static (S) and
linear (L) or nonlinear (N): (4 pt.)
a) y=u2
_S_ _N_
b) y 3 y 5 y u
George W. Woodruff School of Mechanical Engineering
ME3015
Quiz #2 Solutions
Spring 2005
NAME _
1) Draw a free-body diagram of each element of the propeller system shown and derive a differential
equation relating the angular displacement to in. (11)
B
in
George W. Woodruff School of Mechanical Engineering
M3015
Quiz #3 Solutions
Summer 2005
NAME _
1) The linear motion of an automobile including the drag force may be described
by mv bv f where v is the velocity (m/sec), f is the input force (N) transmitted
George W. Woodruff School of Mechanical Engineering
ME3015
Quiz #4 Solutions
Spring 2005
NAME_Key_
1) Consider the mass-spring-damper system given by mx bx kx f .
a. Find the values of m, b and k for which the system
Is critically damped ( =1),
has a natu
Quiz #5 Solutions
ME3015
Summer 2005
NAME _
1) Match the controllers (i-iii) on the left with their intended properties (a-c) on the right. (3)
i.
Proportional Control
a
Eliminates steady-state (offset) error
ii.
Integral Control
b
Improves the speed of t
George W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology
ME3015
HW SET #6
Complete by Friday 7/22/2005
_
1)
2)
3)
4)
5)
Text Problem B-10-6.
Text Problem B-10-8.
Text problem B-10-10.
Text problem B-10-12.
Text problem B-10-13.
George W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology
ME3015A
HW SET #5
Complete by Monday 7/11/2005
_
1) Text Problem B-9-2. In addition, find the steady-sate sinusoidal solution by setting the
exponentially decaying terms t
ME3015 PROBLEM SET #4 (25 points). SOLUTIONS
1. (8 points) Derive the transfer function of the electrical system EO ( s) / Ei ( s) shown below.
Draw a schematic diagram of an analogous mechanical system.
R1
C1
R2
ei(t)
eo(t)
C2
Solution (1)
Define impedan
ME-3015 Exam #1
Name (PRINT)
George W. Woodruff School of Mechanical Engineering
Spring 2012
EXAM #1 ME-3015 SYSTEM DYNAMICS AND CONTROL (A, RCC, RPK, RPY)
February 23rd, 4:35pm 6:25pm
ACADEMIC HONOR CODE: Honor Agreement
Having read the Georgia Institute
ME-3015 Exam #1
Name (PRINT)
George W. Woodruff School of Mechanical Engineering
Spring 2012
Solutions
Problem 1 (70 points)
(a) (10 points)
(b) (20 points)
(c) (20 points)
(d) (20 points)
Problem 2 (30 points)
(30 points)
Problem 3 (50 points)
(a) (10 po
George W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology
ME3015
HW SET #1
Complete by 5/25/2005
_
1) Identify what you consider to be the inputs and outputs for the hot water furnace
shown below:
2) Consider the jackknife mechan
George W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology
ME3015
HW SET #1 Solutions
_
1) Identify what you consider to be the inputs and outputs for the hot water furnace
shown below:
Solution:
Inputs: Qi , Ti , Q f , Qcw , Twi
George W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology
ME3015
HW SET #2
Complete by 6/7/2005
_
1) Text Problem B-3-13.
2) Text Problem B-3-15.
3) Derive a mathematical model for the system shown in the figure 5-45 of the text.
Homework #2 Solution
1) B-3-13
T1
T1
T2
J
T2
k
J
T1
T1 T2
0
k
i
o
b
o
, T2
b
0
Combining these equations,
J
o
k
o
k
i
2) B-3-15
Done in class.
3) Derive a mathematical model for the system shown in the figure 5-45 of the text. Displacements y1 and y2 are
George W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology
ME3015
HW SET #3
Complete by Monday 6/20/2005
_
1)
2)
3)
4)
5)
6)
Text Problem B-4-1.
Text Problem B-4-5.
Text Problem B-6-5.
Text Problem B-6-6.
Problem B-6-10 with capac
George W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology
ME3015A
HW SET #4
Complete by 6/30/2005
_
1) Text problem B-7-3.
2) Text problem B-7-4.
3) Text problem B-7-6 and B-7-7.
4) Text problem B-7-17.
5) Consider the conical ta
George W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology
ME3015A
HW SET #4 Solutions
_
1) Text problem B-7-3.
George W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology
ME3015
HW SET #4 Solutions
_
2) Te
George W. Woodruff School of Mechanical Engineering
Georgia Institute of Technology
ME3015 Sample Final Examination
Spring 2005
NAME _
Problem
Points
I
II
/20
III
/15
IV
/20
V
/25
/20
Total
/100
Please read this first:
1
11 sheet of notes. A Laplace
2
Tra