Questions:
1. Which of the following is not a natural frequency (rad/sec) for this oscillating
system?
a. 3.01
b. 2.145
c. 2.9889
d. 1.121
2. MATLAB produces eigenvectors which have a vector length of one

Class Problems Lesson 15, Fall 2014
Math Methods for Mechanical Engineers (22.361)
1. Solve the following system of linear equations a)using the Gauss Seidel
Method with a stopping criteria of 0.001. b)Create a table which ill

In-Class problem, Lesson 22, Fall 2014
Math Methods for Mechanical Engineers (22.361)
1. Given Class22.xls, import the data into MATLAB and calculate the
mean, range, standard, deviation, variance and coefficient of variation
us

Lesson 8,Fall 2014
Math Methods for Mechanical Engineers (22.361)
Problem 1
Find the minimum of the function y=(x.^2)/10-2*sin(x) for
-10 x 10
Solution:
x=-10:.1:10
function [y] = probL8(x)
%probL8, Use this funct

Class Problems Lesson 16, Fall 2014
Math Methods for Mechanical Engineers (22.361)
1. Solve the following system of nonlinear equations using a) newtmult.m and
b) fsolve
x12+x1x2=10
x2+3x1x22=57
Method a (newtmult)

Lesson 18 Problem, Fall 2014
Math Methods for Mechanical Engineers (22.361)
Given the following equations representing the two mass- three spring
system:
!
!
= ! + (! ! )
!
! !
!
= (! ! ) !
!
!
Assume a solution of

In-Class Linear Regression Problem, Lesson 25, Fall 2014
Math Methods for Mechanical Engineers (22.361)
It is known that the tensile strength of plastic increases as a function of
the time it is heat-treated. The following data

Exercise Lesson 26
, Fall 2012
Math Methods for Mechanical Engineers (22.361)
1. Use the polyfit command to fit a first, second, and third order
polynomial to the following data. In each case plot the curve and the
data.

In-Class Problem, Lesson 23, Fall 2013
Math Methods for Mechanical Engineers (22.361)
1. An insurance company is reviewing its current policy rates. When originally
setting the rates they believed that the average claim amount was $1,800. They are
concern

Exercise Lesson 28, Fall 2014
Math Methods for Mechanical Engineers (22.361)
1. Use the General Linear Least squares method to fit a curve to the
following data.
pH in a reaction varies over a day
t= [0 2 4 5 7 9 12

Class Problems L27
Math Methods for Mechanical Engineers (22.361)
1. General Linear Regression: The following data represents a growth in a crack
length (mm) over a number of days. Find a best-fit equation for the data.

Lesson 29 Problem
Math Methods for Mechanical Engineers (22.361)
Evaluate the following integral:
=
!
2 !
!
a)
b)
c)
d)
e)
f)
4 ! -x +1 dx
analytically
with the trapezoidal rule (n=1)
with a composite application of the tra

Lesson 31 Problem
Math Methods for Mechanical Engineers (22.361)
1. Determine a forward difference and backward difference derivative
approximation with the following data:
y = [20 30 10 50 80 100]
x = [0 5 10 15

Lesson 36 Class Problem, Fall 2014
Math Methods for Mechanical Engineers (22.361)
A steady-state heat balance for a rod is represented as
!
1.5 = 0
!
Obtain a numerical solution for a 10-meter rod with boundary

Lesson 7 Examples,
Math Methods for Mechanical Engineers (22.361)
Given the polynomial f (x ) = x
3 -6x2
+x + 30.
a. Use a graphical method to estimate the roots, you may have to try various x values.
You will realize that this is not that easy.
b.

Homework 12, Fall 2014
Math Methods for Mechanical Engineers (22.361)
A simple tensile test recorded the Fracture Strength (MPa) of 200 specimens of a
carbon fiber composite. The fracture strengths are recorded in H12.xls. I

1. You perform an experiment to measure the yield strength of a material. You take
100 random measurements of the yield strength and obtain the mean of the
sample = 250 MPa Assuming a normal distribution with

Homework 17, Fall 2014
Math Methods for Mechanical Engineers (22.361)
Part 1: You take 50,000 samples of data at a sample frequency of 100 Hertz (100
samples/second). With this data you conduct a discrete Fourier trans

Homework 15, Fall 2014
Math Methods for Mechanical Engineers (22.361)
1. Use least squares regression to fit a straight line to the following data.
X
0
2
4
6
9
11
12
15
17
19
Y
5
6
7
6
9
8
8
10
1

Homework 13, Fall 2014
Math Methods for Mechanical Engineers (22.361)
Part 1: For each of the following problems, perform a hypothesis test clearly showing all 4
steps of the process. Either scan and upload your submission to Blackboard or hand in on
the

Homework 16, Fall 2014
Math Methods for Mechanical Engineers (22.361)
Answer the HW questions on Blackboard and upload all of your plots on one .pdf
document.
1. Given the following data, determine the best-fit coefficie

HW18
Math Methods for Mechanical Engineers (22.361)
1. Given the following integral:
!
= ! 2 ! ! -6x +1 dx
Write a MATLAB script which calculates the following:
a) Ia= analytical Integral
b) I_1=integral with the trapezoi

Homework 19, Fall 2014
Math Methods for Mechanical Engineers (22.361)
Problem 1: Compute the forward and backward difference approximations of O(h)
and O (h2) as well as the central difference approximations of O(h2) and O(h4)

Homework 21, Fall 2014
Math Methods for Mechanical Engineers (22.361)
An insulated heated rod with a uniform heat source can be modeled with the
following equation:
!
= ()
!
Given a heat source = 20oC/m2 and th

Homework 20, Fall 2014
Math Methods for Mechanical Engineers (22.361)
1. The motion of a damped spring-mass system is described by the following
ordinary differential equation: where x=displacement from equilibrium position
(me

1. Use the incremental search method to bracket the roots in the following
function between x=3 and x=6.
y=sin(10*x)+cos(3*x);
Create the function.
Lets call it simple.m
function [y] = simple(x)
0unction

Create the following variables in MATLAB:
a=[1:3]
b=[1:3]'
c=2*ones(3)
d=[1:3;3:5;5:7]
Matrix addition and subtraction: Matrices must be the same size!
try, a+b notice that a+b is not allowed.
Try

Lesson 34 Class Problem, Fall 2014
Math Methods for Mechanical Engineers (22.361)
a. Given the following differential equation:
= ! 1.5
Create a script to solve the initial value problem over the interval t=0 to t=2 w