The University of Texas at San Antonio San Antonio
1013
PHY 010

Spring 2012
Excel in ME  Part 3
Keith A. Woodbury
Mechanical Engineering
University of Alabama
Excel Matrices
There is a built in solver in Microsoft Excel that can produce
almost all the necessary matrix calculations that Matlab is
capable of.
mmult
transpose
minve
The University of Texas at San Antonio San Antonio
1013
PHY 010

Spring 2012
NewtonRaphson Method
Roots of Function using Iterative
Method (Guess solution)
Reading Assignment: Section 6.2
1
NewtonRaphson Method
f(x)
[x f( x )]
f(xi)
i,
i
f(xi )
xi +1 = xi
f (xi )
f(xi1)
xi+2
xi+1
xi
X
Figure 1 Geometrical illustration of the N
The University of Texas at San Antonio San Antonio
1013
PHY 010

Spring 2012
Project 1
1. User interface
2. Options for the user to pick and based on
the response you compute roots of the
equation.
1
You want give user to provide input
before you proceed
help input
INPUT Prompt for user input.
R = INPUT('How many apples') gives th
The University of Texas at San Antonio San Antonio
1013
PHY 010

Spring 2012
Where substantial error is associated with data, polynomial
interpolation is inappropriate and may yield unsatisfactory results when
used to predict intermediate values. Experimentally data is often of this
type. For example, the following figure (a) show
The University of Texas at San Antonio San Antonio
1013
PHY 010

Spring 2012
Roots of Equations
Reading Assignments:
Section 5.1 : Graphical Methods
Section 5.2 Bisection Method
Announcement:
HW 1 on blackboard : Due 9/13 in CLASS.
1
Roots of Equation : Values
of x that makes f(x)=0
ROOTS
2
Example of using Roots of
Equation
Roots
The University of Texas at San Antonio San Antonio
1013
PHY 010

Spring 2012
Class I
Introduction
What is Numerical Methods
What do you think ?
What is Numerical Methods
How to fit straight line ?
Integral of function ?
f(
x
)
y
a
Swing pendulum: Location and velocity at
Statics
Different time instants
b
x
What is Numerical Metho
The University of Texas at San Antonio San Antonio
1013
PHY 010

Spring 2012
PMajor prerequisites by topic:
rerequisites:
Calculus1224
MAT
Differential Equations
TextBooks/Reference/Materi
als
Textbook(s) and/or required material:
Pratap, Getting Started with Matlab Oxford University
Press, 2010, ISBN 9780199731244
Chapra and Can
The University of Texas at San Antonio San Antonio
1013
PHY 010

Spring 2012
RotationalInertia
&
KineticEnergy
Linear&Angular
Linear
Angular
Dis p la c e m e n t
x
Velocity
v
Acceleration
a
Inertia
m
I
KE
mv2
I2
N2
F=ma
=I
Momentum
P=mv
L=I
Rolling Motion
If a round object rolls without slipping, there is a fixed relationship
betw
The University of Texas at San Antonio San Antonio
1013
PHY 010

Spring 2012
Physics 111 HW18
assigned 8 April 2011
1. Angles and arc lengths.
a) What angle in radians is subtended by an arc 1.50 m in length on the circumference of a circle of radius 2.50 m?
What is this angle in degrees?
b) An arc 14.0 cm in length on the circumf
The University of Texas at San Antonio San Antonio
1013
PHY 010

Spring 2012
Simultaneous Linear Equations
Topic: Gaussian Elimination
12/09/12
http:/numericalmethods.eng.usf.e
du
1
Gaussian Elimination
One of the most popular techniques for
solving simultaneous linear equations of the
form [ A ][ X ] = [ C]
Consists of 2 steps
1.
The University of Texas at San Antonio San Antonio
1013
PHY 010

Spring 2012
Final Exam Review
PSI Physics
Multiple Choice
Name_
Kinematics
1.
Suppose that an object is moving with a constant velocity. Make a statement concerning its acceleration.
A) The acceleration must be constantly increasing.
B) The acceleration must be const
The University of Texas at San Antonio San Antonio
1013
PHY 010

Spring 2012
1) When is the average velocity of an object equal to the instantaneous velocity?
A) always
B) never
C) only when the velocity is constant
D) only when the velocity is increasing at a constant rate
2) A new car manufacturer advertises that their car can g
The University of Texas at San Antonio San Antonio
1013
PHY 010

Spring 2012
PHY 2048
Lecture 7
CHAPTER 11
Equlibrium (11.1, 11.2, 11.3)
Equilibrium conditions for a rigid body
First condition: Net external force acting on its center of mass is zero
econd condition: Net torque about any point due to all the external forces is zero
The University of Texas at San Antonio San Antonio
1013
PHY 010

Spring 2012
Chapter 08.07
Finite Difference Method for Ordinary Differential
Equations
After reading this chapter, you should be able to
1. Understand what the finite difference method is and how to use it to solve problems.
What is the finite difference method?
The
The University of Texas at San Antonio San Antonio
1013
PHY 010

Spring 2012
DifferentiationContinuous
Functions
How to obtain 1st and 2nd derivative of a
function numerically ?
Finite Differences
1
Numerical Differentiation
Chapter 23
Differentiation Continuous
Functions
3
Graphical Representation Of
Forward Difference
Approxima
The University of Texas at San Antonio San Antonio
1013
PHY 010

Spring 2012
Project 1
1. User interface
2. Options for the user to pick and based on
the response you compute roots of the
equation.
1
You want give user to provide input
before you proceed
help input
INPUT Prompt for user input.
R = INPUT('How many apples') gives th
The University of Texas at San Antonio San Antonio
1013
PHY 010

Spring 2012
Project 1
1. User interface
2. Options for the user to pick and based on
the response you compute roots of the
equation.
1
You want give user to provide input
before you proceed
help input
INPUT Prompt for user input.
R = INPUT('How many apples') gives th
The University of Texas at San Antonio San Antonio
1013
PHY 010

Spring 2012
function forward
clc
clear all
function k=f(x)
k=x.^22;
end
%
Declaring 'x' as a variable
x = sym('x','real');
%
Value of x at which f '(x) is desired, xv
xv=4;
%
Starting step size, h
h=0.2;
%
Number of times starting step size is halved
n=12;
Soln=diff
The University of Texas at San Antonio San Antonio
1013
PHY 010

Spring 2012
Physics 111 HW 27
assigned 7 December 2011
PP01. A 1.80 kg monkey wrench is pivoted 0.250 m from its center of mass and allowed to swing as a
physical pendulum. The period for smallangle oscillations is 0.940 s.
a) What is the moment of inertia of the wr