From 40eb941a6fd69b6cecce96166a03d7fb60f181a4 Mon Sep 17 00:00:00 2001 From: "Ryan C. Cooper" Date: Thu, 26 Oct 2017 14:26:50 -0400 Subject: [PATCH] updated extra credit and HW4 readmes --- HW4/README.html | 84 ----------------------------------------- HW4/README.md | 2 +- HW4/README.pdf | Bin 172036 -> 0 bytes extra_credit/README.md | 2 +- 4 files changed, 2 insertions(+), 86 deletions(-) delete mode 100644 HW4/README.html delete mode 100644 HW4/README.pdf diff --git a/HW4/README.html b/HW4/README.html deleted file mode 100644 index 67d8735..0000000 --- a/HW4/README.html +++ /dev/null @@ -1,84 +0,0 @@ - - - - - - - - - - - -

Homework #4

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final commit due 11/2/17 by 11:59pm

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Include all work as either an m-file script, m-file function, or example code included with ``` and document your code in the README.md file

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  1. Create a new github repository called ‘04_linear_algebra’.

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    1. Add rcc02007 and zhs15101 as collaborators.

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    3. Clone the repository to your computer.

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    5. Complete this before 10/26 by midnight

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P2 Due 10/26

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  1. Create the 4x4 and 5x5 Hilbert matrix as H. Include the following results in your README before 10/26 by midnight:
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  1. What are the 2-norm, frobenius-norm, 0-norm and infinity-norm of the 4x4 and 5x5 Hilbert matrices?

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  3. What are the 2-norm, frobenius-norm, 0-norm and infinity-norm of the 4x4 and 5x5 inverse Hilbert matrices?

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  5. What are the condition numbers for the 2-norm, frobenius-norm, 0-norm and infinity-norm of the 4x4 and 5x5 Hilbert matrices?

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P3-4 Due 10/30

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  1. Create a Cholesky factorization function called chol_tridiag.m that takes 2 vectors as inputs and calculates the Cholseky factorization of a tridiagonal matrix. The output should be 2 vectors, the diagonal and the off-diagonal vector of the Cholesky matrix.

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    [d,u]=chol_tridiag(e,f);

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  3. Use the output from chol_tridiag.m to create a forward substitution and back-substitution function called solve_tridiag.m that provides the solution of Ax=b given the vectors from the output of [d,u]=lu_tridiag(e,f). Note: do not use the backslash solver \, create an algebraic solution

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    x=solve_tridiag(d,u,b);

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-Spring-mass system for problem 5 -

Spring-mass system for problem 5

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  1. Create the stiffness matrix for the 4-mass system shown above for cases a-c. Calculate the condition of the stiffness matrices. What is the expected error when calculating the displacements of the 4 masses? Include the analysis and results in your README.
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  1. K1=K2=K3=K4=1000 N/m

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  3. K1=K3=K4=1000 N/m, K2=1000e12 N/m

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  5. K1=K3=K4=1000 N/m, K2=1000e-12 N/m

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  1. Use chol_tridiag.m and solve_tridiag.m to solve for the displacements of hanging masses 1-4 shown above in 5a-c, if all masses are 1 kg.
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-Spring-mass system for analysis -

Spring-mass system for analysis

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  1. In the system shown above, determine the three differential equations for the position of masses 1, 2, and 3. Solve for the vibrational modes of the spring-mass system if k1=10 N/m, k2=k3=20 N/m, and k4=10 N/m. The masses are m1=1 kg, m2=2 kg and m3=4 kg. Create a function, mass_spring_vibrate.m that outputs the vibration modes and natural frequencies based upon the parameters, k1, k2, k3, and k4.

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  3. The curvature of a slender column subject to an axial load P can be modeled by

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\(\frac{d^{2}y}{dx^{2}} + p^{2} y = 0\)

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where \(p^{2} = \frac{P}{EI}\)

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where E = the modulus of elasticity, and I = the moment of inertia of the cross section about its neutral axis.

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This model can be converted into an eigenvalue problem by substituting a centered finite-difference approximation for the second derivative to give \(\frac{y_{i+1} -2y_{i} + y_{i-1} }{\Delta x^{2}}+ p^{2} y_{i}\)

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where i = a node located at a position along the rod’s interior, and \(\Delta x\) = the spacing between nodes. This equation can be expressed as \(y_{i-1} - (2 - \Delta x^{2} p^{2} )y_{i} +y_{i+1} = 0\) Writing this equation for a series of interior nodes along the axis of the column yields a homogeneous system of equations. (See 13.10 for 4 interior-node example)

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Determine the eigenvalues for a 5-segment (4-interior nodes), 6-segment (5-interior nodes), and 10-segment (9-interior nodes). Using the modulus and moment of inertia of a pole for pole-vaulting ( http://people.bath.ac.uk/taf21/sports_whole.htm) E=76E9 Pa, I=4E-8 m^4, and L= 5m.

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Include a table in the README.md that shows the following results: What are the largest and smallest loads in the beam based upon the different shapes? How many eigenvalues are there?

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| # of segments | largest load (N) | smallest load (N) | # of eigenvalues |
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-| 5 | ... | ... | ... |
-| 6 | ... | ... | ... |
-| 10 | ... | ... | ... |
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If the segment length approaches 0, how many eigenvalues would there be?

- - diff --git a/HW4/README.md b/HW4/README.md index fb5bd15..ae98f2c 100644 --- a/HW4/README.md +++ b/HW4/README.md @@ -24,7 +24,7 @@ README before 10/26 by midnight: b. What are the 2-norm, frobenius-norm, 1-norm and infinity-norm of the 4x4 and 5x5 inverse Hilbert matrices? - c. What are the condition numbers for the 2-norm, frobenius-norm, 0-norm and + c. 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zlv+kpUq*4HAKO0TkES6g*NZ0qs$pifrm41Oh%KXf936^9gm5E5FQY!N{YmFxwYq>4 zr&SRb?OA+s_+n$f-`Qv%@rxs_@saNmny1ua!C-6LS@}~FIVE1+wIL@`VRp0;s diff --git a/extra_credit/README.md b/extra_credit/README.md index e6e57c2..0ac65ae 100644 --- a/extra_credit/README.md +++ b/extra_credit/README.md @@ -10,7 +10,7 @@ Save your progress report and put it in a repository called 'ME3255-Extra_Credit # Extra Credit Assignment \#2 ## Due 11/1 by 11:59 pm -Find a dartboard [UConn gameroom](http://studentunion.uconn.edu/game-room/). And tack the +Find a dartboard e.g. [Sports Bar](https://www.yelp.com/biz/the-sports-bar-north-windham). And tack the following [polar_graph.pdf](./polar_graph.pdf) to the dartboard. Throw 10 darts (that hit the board) and record the radius and angle that the dart hit the target in a csv file in your 'ME3255-Extra_Credit' repository called `data.csv`. Organize the csv file in