Expert answer:Numerical-Methods/mathematica
Solved by verified expert:I need solving this project by mathematica code and write report as in the filei need it within 40 hrs max
numeircalmethods.pdf
Unformatted Attachment Preview
PROJECT 1: BUNGEE CORD
Due: Dec 1, 2017 at 3:30 pm (electronic submission only)
Course: Numerical Methods 2017
Instructor: Dr. Hooman Tafreshi
Consider a 1 m long flexible cord (e.g., bungee cord) represented with an array of 13 point‐masses connected to one another
by springs and dampers as shown in Figure 1.
y
2
1
3
4
5
6
7
8
9
10
11
12
13
x
Figure 1: Mass‐Spring‐Damper (MSD) representation of a flexible chain.
The forces acting on a point mass are shown in the free body diagram illustrated in Figure 2. In addition to gravity, there
are spring and damper forces that act on each point‐mass. Expressions for these forces are listed below:
(
,
(
)
( ,
,
)
)
Figure 2: Free body diagram illustrating forces acting on point mass i.
s
f i ,i 1 ks pi pi 1 lr
s
f i ,i 1 ks pi pi 1 lr
pi pi 1
pi pi 1
p p
(1)
i
i 1
pi pi 1
(2)
d
f i ,i 1 kd u i u i 1
(3)
d
f i ,i 1 kd u i u i 1
(4)
s
d
s
d
where f i ,i 1 , f i ,i 1 , f i ,i 1 , and f i ,i 1 are the spring and damper forces acting on point‐mass by its neighboring point‐
masses, and p i , pi 1 , and pi 1 are the position vectors of point‐masses ,
1, and
1, respectively. ks and kd are the
spring and damping constants, respectively. The un‐stretched length of the springs is shown with and it is equal to 0.1 m.
1
The velocity vectors for point‐masses ,
1, and
distance between neighboring point‐masses are
1, are shown with u i , u i 1 , and u i 1 , respectively. The instantaneous
pi pi 1
xi xi 1
2
yi yi 1
2
(5)
p i p i 1
xi xi 1
2
yi yi 1
2
(6)
Therefore, the fractions on the right‐hand side of Equations 1 and 2 are the unit vectors for the distance between the
corresponding point‐masses. The position and velocity of the point‐mass can be obtained by solving Newton’s 2nd law
written for each point‐mass:
p i p i 1
p i p i 1
mai ks p i p i 1 lr
k s p i p i 1 lr
p i p i 1
p i p i 1
(7)
kd u i u i 1 kd u i u i 1 mg
where g is the gravitational acceleration, a i is the acceleration of the point‐mass , and m is the mass of each point‐
mass. The above equation can be solved for any point‐mass 2
12. See [1] for more information.
What you should submit:
1. Develop a Mathematica code that solves the above equations for each point‐mass.
2. Assume zero initial velocity and zero stretching for the cord. Plot the profile and velocity of the cord (the x y
coordinates and velocity of each point‐mass) when it falls under gravity at 10 different times starting from t=0
until the system stops moving (steady‐state position) for k s / m and kd / m values of 100 N / m.kg and 10
N .s / m.kg , respectively.
3. Repeat step 2 but for when the cord has an upward parabolic initial velocity with a peak value of 10 m/s.
4. Repeat step 2 but for when the cord is initially pull up from the middle to a height of 0.5 m above the resting
position.
5. Write a short, but yet clean and professional report describing your work. Up to 25% of your grade will be based
solely on the style and formatting of your report. Use proper heading for each section of your report. Be consistent
in your font size. Use Times New Roman only. Make sure that figures have proper self‐explanatory captions and are
cited in the body of the report. Make sure that your figures have legends as well as x and y labels with proper and
consistent fonts. Don’t forget that any number presented in the report or on the figures has to have a proper unit.
Equations and pages in your report should be numbered. Embed your figures in the text. Make sure they do not
have unnecessary frames around them or are not plotted on a grey background (default setting of some software
programs!).
Note: While you can work together on your projects, what you submit should be YOUR OWN original work.
References:
1‐D.G. Venkateshan, M.A. Tahir, H.V. Tafreshi, and B. Pourdeyhimi, Modeling Effects of Fiber Rigidity on Thickness and
Porosity of Virtual Electrospun Mats, Materials and Design, 96, 27 (2016)
2
…
Purchase answer to see full
attachment
How it works
- Paste your instructions in the instructions box. You can also attach an instructions file
- Select the writer category, deadline, education level and review the instructions
- Make a payment for the order to be assignment to a writer
- Download the paper after the writer uploads it
Will the writer plagiarize my essay?
You will get a plagiarism-free paper and you can get an originality report upon request.
Is this service safe?
All the personal information is confidential and we have 100% safe payment methods. We also guarantee good grades