SAM P L E EX A M
Final Examination GE 85-111 Page 1 of 10
(10 Marks) 1. (a) By the method of 'oints determine the bar forces in bars AB, AH,
BH, HG, BG and BC. (Note that the reactions
Chapter 2
Static and Dynamic Characteristics
of Signals
Instructor: Dr. M. Mustafa Akbari
Department of Mechanical Engineering
In chapter1, you learned the following main topics:
Basic Concepts of M
Chapter 2
Static and Dynamic Characteristics
of Signals
Instructor: Dr. M. Mustafa Akbari
Department of Mechanical Engineering
In chapter1, you learned the following main topics:
Basic Concepts of M
Chapter 3
Pure substance:
a substance that has a fixed chemical composition throughout.
Ex: water, nitrogen, helium, and carbon dioxide.
Compressed or Subcooled liquid:
Superheated vapor:
in the liqui
PROBLEM 3.1
KNOWN:
K = 2 V/kg
F(t) = constant = A
Possible range of A: 1 kg to 10 kg
FIND:
y(t)
SOLUTION
We will model the input as a static value and interpret the static output that results. To do
t
PROBLEM 2.1
FIND: Define signal and provide examples of static and dynamic input signals to
measurement systems.
SOLUTION: A signal is information in motion from one place to another, such as
between
Chapter 6 (2nd law of thermodynamic)
Difference between 1st and 2nd law of thermodynamics:
The first law is concerned with the quantity of energy and the transformations of energy from one form
to ano
Examples: Find the partial derivatives of the following functions.
1. f (x, y) =
p
x2
y 2 = (x2
y 2 )1/2
solution: For each of the partial derivatives we use the general power rule:
1
fx = (x2
2
y2)
1
Examples:
1. Find all critical points of f (x, y) = 2x2 + y 2 + 8x
6y + 20.
solution: We nd the partial derivatives and set them equal to 0
fx = 4x + 8 = 0
fy = 2y
These imply that x =
6=0
2 and y = 3
This is a disk of radius 4 centered at the origin.
For another example, let
f (x, y) =
(x
4
2)(y
3)
This function is dened unless x = 2 or y = 3. So the domain will be entire xy-plane except
for the f
0
0.1
Precalculus Review
Real Line and Order
When discussing order on the real number line, we use the following symbols:
<
>
less than
less than or equal to
greater than
greater than or equal to
7
Functions of Several Variables
Suppose you run a company which produces two types of television. Let x1 be the quantity
of type 1 and x2 be the quantity of type 2. Then the usual functions in which
UNIVERSITY OF WINDSOR
Civil and Environmental Engineering
GE 85-111
E . . H l . I
Mid-Term Test
October 22, 1997
Students Name: ___________
Students ID. No.: ___________________
Group No.: ________
Chapter 2
Static and Dynamic Characteristics
of Signals
Instructor: Dr. M. Mustafa Akbari
Department of Mechanical Engineering
In chapter1, you learned the following main topics:
Basic Concepts of M