JME 3710
August 29, 2013
Homework #1 Solutions
1. (10 pts) At some instant in time, the temperature distribution within a particular onedimensional
domain 0 x 3 L is known to be
T (x) = T0
x3
3 x2
2x
+ 1
+
3
2
3L
2L
L
,
where T0 and L are constant referen
Homework Set # 09 Solutions
Fall 2013 Control Systems I
Name: _
Aux50 By inspection only and without using RouthHurwitz, list which characteristic equations
(C.E.)a, b, c, or d have either Right Half Plane poles or Imaginary Axis poles (RHP and/or IA)
Homework Solution Set # 3  Solutions
Fall 2013 Control Systems I
Name: _
Aux12
OgataP111
Using Masons rule, write the transfer function C/R for the Flow Graph shown
below.
Solution Aux 12
M1 G1G2G3G4G5
1 1
M 2 G1G6G4G5
2 1
M 3 G1G2G7
3 1 G4 H1
L1 G4 H1
Homework Set #8 Solutions
Fall 2013 Control Systems I
Name: _
Aux43 a) Find the steady state error for E(s), the output of the summing junction, for a unit step
input at R(s). This value is the difference between the output, C(s), and what was commanded
Homework Set # 10 Solutions
Fall 2013 Control Systems I
Name: _
Aux56 Using RouthHurwitz Criterion, determine if the following Characteristic Equation (C.E.) is
stable, marginally stable, or unstable. That is, does it have roots in the RHP, LHP, or on
Homework Set #2  Solutions
Spring 2013 Control Systems 1
Name: _
Aux 07 Write the transfer function C(s)/R(s) for the block diagram shown below. Suggestion,
use Masons rule.
R(s)
+

G1
+
H3
+
G2
C(s)
+

G3
G4
H2
H1
Solution P3
G1G 2 G3 G 4
C (s)
R( s )
Homework Set # 12 Solutions
Spring 2013 Control Systems I
Name: _
Aux70 For the control system with the loop gain G(s)H(s) given below a) Draw the Root Locus
diagram. b) Calculate the value of K that such that the system becomes marginally stable. c)
Ca
Solutions Homework Set #13
Summer 2013 Control Systems 1
Name: _
Aux_75 Sketch a straight line approximation of the Bode Gain vs Frequency plot for the transfer
function given.
Aux_75 Solution
First convert the transfer function to a (s + 1) format.
From
Homework Set # 4  Solutions
Fall 2013 Control Systems I
Name: _
Aux18 For the following transfer functions state if the system is overdamped,
critically damped, under damped, marginally stable, or unstable. Also state where
the roots are located jusifyi
Homework Set #11 Solutions
Spring 2013 Control Systems 1
Name: _
Aux63
Dorf E6.24
Consider the system represented in state variable form
x Ax Bu
where
y Cx Du
0 1 0
0
A= 0 0 1 B= 0 C= 1 0 0 D= 0
k k k
1
a) Determine the system transfer function G(s) u
Homework Set #6  Solutions
Spring 2013 Control Systems 1
Name: _
Aux_32 Draw the flow graph for the following transfer function by
means of direct decomposition. Assign the state variables x1, x2, x3, and
x4 in the diagram.
G( s)
C (s)
10( s 2)
2
U ( s
Homework Set #7 Solution
Fall 2013 Control Systems I
Work problems on a printout of this document. Enter answers in boxes provided
NAME: _
AUX_37 a) Find the steady state error for E(s), the output of the summing junction, for a unit
step input at R(s).
Homework Set #5  Solutions
Spring 2013 Control Systems 1
Name: _
Aux25 For the two systems with the input r(t) and output y(t) that are described by the
Y (s)
following differential equations, find the Laplace transfer function T ( s )
for each system
(These notes refer to Chapter 1 of the text Engineering Ethics: Concepts and Cases, 4th
edition, Harris, Pritchard, and Rabins, ThomsonWadsworth, 2009)
There are some occupations (e.g., physicians or lawyers) we would say are undeniably
professions and o
JME 3710
October 3, 2013
Homework #6 Solutions
1. (10 pts) Certain thin metallic coatings can be deposited by
shooting workpieces with molten metal droplets, which are
sprayed from a nozzle and travel through an inert gas shield to
prevent oxidation on th
JME 3710
October 14, 2013
Homework #7 Solutions
1. (10 pts) Fig. 1 shows a simple model of nuclear
power generation: a nuclear fuel rod surrounded
by owing water within a tube. The tube has a
length L and is wellinsulated and the rod has a
diameter D. The
JME 3710
October 17, 2013
Homework #8 Solutions
1. (10 pts) Liquid metal ows along axis x through a square crosssection duct of side length 2a.
As a rst approximation, the velocity prole is uniform, i.e. u(y, z) = C1 and the temperature
prole is
z 2
y 2
T
JME 3710
November 7, 2013
Homework #9 Solutions
1. (10 pts) A very long concentrictube heat exchanger (singlepass) has hotside and coldside
inlet temperatures of Ti h = 100o C and Ti c = 10o C, respectively. If (mcp )h = 2 (mcp )c ,
determine the hots
JME 3710
November 12, 2013
Homework #10 Solutions
1. (10 pts) A simple concentrictube heat exchanger uses hot oil to heat cold water. Mass ow
rates on both sides are 0.05 kg/s. The design temperature change on the cold side is Ti c =
300 K To c = 370 K
JME 3710
September 19, 2013
Homework #4 Solutions
1. (10 pts) A thermocouple of main length dimension D is to be
designed and constructed. In this particular problem, there
are 2 choices: a spherical shape, where the diameter is D, or
a cube shape, where
JME 3710
September 5, 2013
Homework #2 Solutions
1. (10 pts) A common task in architecture and
construction is estimation of heat loads for
a building. A simple wall has dimensions
W H = 10 m 3 m and a single window of dimensions w h = 0.7 m 1 m
(Fig. 1).
JME 3710
September 26, 2013
Homework #5 Solutions
1. (10 pts) A particular boundarylayer ow over a at plate exhibits a steady temperature prole
of T (y) = C0 + C1 y + C2 y 2 + C3 y 3 , where y is the vertical height above the plate and
C0 . . . C3 are all
JME 3710
September 14, 2013
Homework #3 Solutions
k
perfect
insulation
1. (10 pts) Conduction occurs onedimensionally in
a slab having constant conductivity k and constant heat generation q (Fig. 1). Calculate the
temperature distribution T (x) in 0 x L i
CES EduPack Exercises with Worked Solutions
E8 Multiple constraints and objectives
Overconstrained problems are normal in materials selection. Often it
is just a case of applying each constraint in turn, retaining only those
solutions that meet them all.