MATLAB assignment
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Note that to complete this assignment, you will be asked to write a structure plan / pseudocode for each
problem. The structure will be similarly to the “Given/Find” format you are familiar with from other
homework assignments. Similarly, actually writing functioning code will fulfill the “Solution” portion of
the problem-solving format. It is expected that you use MATLAB to test your script files.
Problem 1 (5 points) (modified version of Exercise 8.13 from textbook, page 126)
A projectile is launched from the point O with an initial velocity of 55 m/s at an angle of 50 degrees to the
horizontal. Write a program which computes and displays the time in the air, and horizontal and vertical
displacement from the point O every 0.5 seconds, as long as the projectile remains above a horizontal plane
through O.
Hints:
• Use a while loop for this problem.
• Use the disp() function to display the results in table format. The char() function can be used within
the disp() to make the columns line up nicely. For example:
disp([‘t = ‘,num2str(t),char(9),char(9),’x = ‘,num2str(x,’%10.1f’)])
Deliverables:
• Hardcopy of your M-file containing your structure plan describing how you plan to solve the
problem along with your executable code.
Problem 2 (10 points) (Problem 3 from Homework 4)
Recall the vertical tank problem from Homework 4. (See Homework 4 for details).
For this homework assignment, plot Volume and Weight as a function of height of solid in the tank (put
height on x-axis). Set the bounds and major gridlines such that the data series for volume and weight are
superimposed on each other. Assume the following parameters:
a. Total height of the tank: ℎ = 20 ????
b. Diameter of the cylinder: ?? = 10 ????
c. Angle of the cone: ?? = 35 ??????????????.
d. Bulk density of solid contents: ?? = 25 ??????.
Hint: If you want dual y-axis, the book recommends using plotyy(), but this is not recommended. Check
online documentation for plotyy() and it will link to yyaxis, a better solution.
Deliverables:
• Hardcopy containing the following:
o Your M-file containing your structure plan describing how you plan to solve the problem
along with your executable code.
o Figure showing the plot of the data.
iPad الخاص بـ abdulaziz
iPad الخاص بـ abdulaziz
Problem 3 (10 points) (modified version of Exercise 9.1 from textbook, page 232)
Draw a graph of the population of the USA from 1790 to 2000 using the (logistic) model:
??(??) =
197,273,000
1 + ??−0.03134(??−1913.25)
where t is the date in years.
Actual data (in 1000s) for every decade from 1790 to 1950 are as follows:
Years Population (in 1000s)
Years Population (in 1000s)
Years Population (in 1000s)
1790 3,929 1850 23,192 1910 91,972
1800 5,308 1860 31,443 1920 105,711
1810 7,240 1870 38,558 1930 122,775
1820 9,638 1880 50,156 1940 131,669
1830 12,866 1890 62,948 1950 150,697
1840 17,069 1900 75,995
Superimpose this data on the graph of P(t). Plot the data as discrete circles (i.e. do not join them with lines).
Hint: Your plot should look similar to Figure 9.16 on page 233 of the textbook.
Deliverables:
• Hardcopy containing the following:
o Your M-file containing your structure plan describing how you plan to solve the problem
along with your executable code.
o Figure showing the plot of the data.
Problem 4 (15 points) (modified version of Exercise 8.12 from textbook, page 195)
A student borrows $10,000 to buy a used car. Interest on her loan is compounded at the rate of 2% per
month while the outstanding balance of the loan is more than $5000, and at 1% per month otherwise. She
pays back $400 every month, except for the last month, when the repayment must be less than $400. She
pays at the end of the month, after the interest on the balance has been compounded. The first repayment is
made one month after the loan is paid out. Write a program which displays a monthly statement of the
balance (after the monthly payments has been made), the final payment, and the month of the final payment.
Hint: Use a while loop for this problem.
Deliverables:
• Hardcopy of your M-file containing your structure plan describing how you plan to solve the
problem along with your executable code.
Name _________________________________________
Last, First
Problem 1 (5 pts)
Below Avg. (4 pts) Average (7 pts) Excellent (10 pts)
Points
Problem attempted, but
incorrect, and poor
attempt at structure plan.
Solution has minor errors or
incomplete structure plan.
Correct numerical solution.
Well documented M-file &
structure plan.
Problem 2 (10 pts)
Below Avg. (4 pts) Average (7 pts) Excellent (10 pts) Points
Problem attempted, but
incorrect, and poor
attempt at structure plan.
Solution / plot has minor errors or
incomplete structure plan.
Correct solution numerical
solution with well-presented
plot.
Well documented M-file &
structure plan.
Problem 3 (10 pts)
Below Avg. (4 pts) Average (7 pts) Excellent (10 pts) Points
Problem attempted, but
incorrect, and poor
attempt at structure plan.
Solution / plot has minor errors or
incomplete structure plan.
Correct solution numerical
solution with well-presented
plot.
Well documented M-file &
structure plan.
Problem 4 (15 pts)
Below Avg. (4 pts) Average (7 pts) Excellent (10 pts) Points
Problem attempted, but
incorrect, and poor
attempt at structure plan.
Solution has minor errors or
incomplete structure plan.
Correct numerical solution.
Well documented M-file &
structure plan.
General Requirements (10 pts)
Requirement Unacceptable (5 pts)
Expected
(10 pts)
Points
Use provided cover sheet.
If any of the
requirements are
missing or do not
meet specification.
All format
requirements
met.
Header on each page (Course, Assignment, Name, page #).
Single sided print copy.
Each problem on a new page (single sided).
Pages in correct order.
One staple in the upper left corner.
Final answers boxed / highlighted.
Clear / Neat formatting.
Excel file submitted to D2L.
Total Score
/50
Problem 1 (5 points) (modified version of Exercise 8.13 from textbook, page 126)
Problem 2 (10 points) (Problem 3 from Homework 4)
Problem 3 (10 points) (modified version of Exercise 9.1 from textbook, page 232)
Problem 4 (15 points) (modified version of Exercise 8.12 from textbook, page 195)
Problem 1 (5 pts)
Problem 2 (10 pts)
Problem 3 (10 pts)
Problem 4 (15 pts)
General Requirements (10 pts)
Alternative Width (in)
Height
(in)
Number
of Bars
Bar
Size
#1 12 24 3 #9
#2 15 15 6 #8
#3 10 24 4 #8
#4 10 23 3 #8
#5 11 26 5 #7
#6 12 30 6 #6
#7 12 19 3 #10
#8 10 30 8 #5
Table 2: US Rebar Size Chart
Bar
Size
Unit Weight
(lb/ft)
Nominal Diameter
(in)
Nominal Area
(in2)
#2 0.167 0.250 0.50
#3 0.376 0.375 0.11
#4 0.668 0.500 0.20
#5 1.043 0.625 0.31
#6 1.502 0.750 0.44
#7 2.044 0.875 0.60
#8 2.670 1.000 0.79
#9 3.400 1.128 1.00
#10 4.303 1.270 1.27
#11 5.313 1.410 1.56
#14 7.650 1.693 2.25
#18 13.60 2.257 4.00
Problem 2 (5 points)
In your statics analysis class, you have established the following set of equilibrium equations:
0.286?????? − 0.428?????? + 0.707?????? = 0
−0.428?????? − 0.286?????? + 0.385?????? = 0
−0.857?????? − 0.857?????? − 0.923?????? + 0.707?????? = 0
You are told that ?????? = −1000??????. Use Excel to determine the value of the remaining three unknowns.
In your solution, report the value of each unknown to 3 decimal places.
Figure 1. Problem 3 sketch.
Problem 3 (15 points)
Vertical tanks with a conical base are often used for storing solids such
as grain, salt, and gravel. The sloping sides prevent plugging as the
material is withdrawn. The height of the tank is ℎ, and the height of the
conical section is ℎ??. The diameter of the tank is ?? and the radius of the
conical section is ??. The angle of the conical section is ??. For this
example, assume that this angle is 35 ??????????????.
If the height of the solid in the tank is less than the height of the conical
section, ℎ??, then the volume is computed using the formula for the
volume of a cone.
?? =
1
3
????2ℎ
However, if the tank is filled to a depth greater than ℎ??, the volume is
the sum of the conical section and the volume of the cylinder.
The volume of the cylinder section is
?? = ?? �
??
2
�
2
(ℎ − ℎ??)
Hence, the total volume is the sum of the two sections of the material has a depth greater than ℎ??.
The radius of the conical section, ??, depends on the value of ℎ. If ℎ < ℎ??, then ?? = ℎ ??????(??), otherwise
it is just ??/2.
Also, we often need to know the weight of the bulk material in the tank. The bulk density includes the
solid material and the air voids between the grains.
For this problem, perform the following calculations:
a) Develop a table at 1 ft intervals that summarizes the volume of the tank and the weight of its
contents. As a minimum you must use the IF, MIN, and MAX functions. Assume the following
parameters:
a. Total height of the tank: ℎ = 20 ????
b. Diameter of the cylinder: ?? = 10 ????
c. Angle of the cone: ?? = 35 ??????????????.
d. Bulk density of solid contents: ?? = 25 ??????.
b) Plot Volume and Weight as a function of height of solid in the tank (put height on x-axis). Set the
bounds and major gridlines such that the data series for volume and weight are superimposed on
each other.
c) Suppose that you would like to know the overall height (to four decimal places) of the tank with
an exact volume of 1500 ft3. Use Goal Seek to determine the overall height. In your solution,
make if very clear which cells you are using for input to the Goal Seek function.
Problem 4 (10 points)
Meteorological data for a water quality and hydrodynamic model of the Dead Sea in Israel/Jordan was
developed for the time period 1993-2001. These data include air temperature (oC), dew point temperature
(oC), wind speed (m/s) and direction (radians), cloud cover (0-10), and short wave solar radiation (W/m2).
This data may be found in a text document H4.txt found on D2L
For this Problem, you do not need to follow the usual Give/Find/Solution. Simply report the Table As
described in Part A and the plot as described in Part B. DO NOT PRINT THE FULL DATA SET.
Part A: Using Descriptive Statistics
Use Data/Data Analysis/Descriptive Statistics to give you a table with the following variables for wind
speed over the entire time period as shown below.
Mean
Standard Error
Median
Mode
Standard Deviation
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Sum
Count
Part B: Histogram
Plot a histogram of the wind speed values showing frequency and cumulative % using the Histogram
function. One way to do this is to use Data/DataAnalysis/Histogram. You must decide on the “bin” size of
the wind speed and set up an area in your sheet where you outline them (You must specify your own bin
size. Do not use the Excel default.).
As an example, the graph in Figure 2 for air temperature used the bins: 10, 12.5, 15, 17.5, etc. A
combined column cluster with a line (see under Custom graphs) was also used.
Figure 2: Histogram of air temperature in the Dead Sea between 1993 and 2001
0
%
50%
100%
150%
0
10000
20000
30000
40000
50000
10
12
.5 15
17
.5 20
22
.5 25
27
.5 30
32
.5 35
37
.5 40
M
or
e
Cu
m
ul
at
iv
e
%
Fr
eq
ue
nc
y
Air temperature, oC
Dead Sea Air Temperature
Frequency
Cumulative %
Name _________________________________________
Last, First
Problem 1 (10 pts)
Below Avg. (5 pts) Average (7.5 pts) Excellent (10 pts)
Points
Problem attempted, but
incorrect, poorly
documented solution.
Solution has minor errors or
incomplete summary of approach.
Correct answer with all
general equations provided.
Problem 2 (5 pts)
Below Avg. (2.5 pts) Excellent (5 pts) Points
Problem attempted, but incorrect answer or
poorly organized.
Correct answers.
Clear, concise organization.
Problem 3 (15 pts)
Below Avg. (6 pts) Average (9 pts) Good (12 pts) Excellent (15 pts) Points
Solution has many
major errors, with
improper approach that
is difficult to follow.
No table or plot
provided.
Goal seek not used.
No discussion provided.
Incomplete solution.
Solution has notable
errors or
misunderstanding of
approach.
Table and/or plot have
major error(s)
Goal seek was used
incorrectly or not at all.
All work shown, but
may be difficult to
follow.
Solution has minor
error(s). In general,
proper approach with
general equations
shown.
Table and/or plot have
minor error(s) or goal
seek may have been
used incorrectly.
All work shown.
Correct answer(s)
including units & sig
figs. Proper approach
with general equations
shown.
Table & plot include
units and labels.
Goal Seek used
correctly.
All work shown and
easy to follow.
Problem 4 (10 pts)
Below Avg. (5 pts) Average (7.5 pts) Excellent (10 pts) Points
Problem attempted, but
incorrect table and plot.
Only one of the following is correct:
** Descriptive statistic table
** Histogram
Both correct descriptive
statistics table and histogram
General Requirements (10 pts)
Requirement Unacceptable (5 pts)
Expected
(10 pts)
Points
Use provided cover sheet.
If any of the
requirements are
missing or do not
meet specification.
All format
requirements
met.
Header on each page (Course, Assignment, Name, page #).
Single sided print copy.
Each problem on a new page (single sided).
Pages in correct order.
One staple in the upper left corner.
Final answers boxed.
Solutions follow Given/Find/Solve format.
Clear / Neat formatting.
Total Score
/50
- Problem 1 (10 points)
- Figure 1: Example Reinforced Concrete Beam
- Problem 1 (10 points) (Cont.)
Problem 2 (5 points)
Problem 3 (15 points)
Problem 4 (10 points)
Figure 2: Histogram of air temperature in the Dead Sea between 1993 and 2001
Problem 1 (10 pts)
Problem 2 (5 pts)
Problem 3 (15 pts)
Problem 4 (10 pts)
General Requirements (10 pts)
