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fix numbering hw4
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rcc02007 committed Oct 31, 2017
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Expand Up @@ -15,7 +15,7 @@ with \`\`\` and document your code in the README.md file*
c. Submit clone repo link to
[https://goo.gl/forms/gFNxhNM4qJJKj8hE3](https://goo.gl/forms/gFNxhNM4qJJKj8hE3)

2. Create the 4x4 and 5x5 [Hilbert matrix](https://en.wikipedia.org/wiki/Hilbert_matrix) as H. Include the following results in your
**2\.** Create the 4x4 and 5x5 [Hilbert matrix](https://en.wikipedia.org/wiki/Hilbert_matrix) as H. Include the following results in your
README before 10/26 by midnight:

a. What are the 2-norm, frobenius-norm, 1-norm and infinity-norm of the 4x4 and 5x5
Expand All @@ -29,22 +29,22 @@ README before 10/26 by midnight:

### P3-4 Due 10/30

3. Create a Cholesky factorization function called `chol_tridiag.m` that takes 2 vectors
**3\.** 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.

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

4. Use the output from `chol_tridiag.m` to create a forward substitution and
**4\.** 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*

```x=solve_tridiag(d,u,b);```
```x=solve_tridiag(d,u,b);```

![Spring-mass system for problem 5](./figures/mass_springs.png)

5. Create the stiffness matrix for the 4-mass system shown above
**5\.** 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.

Expand All @@ -54,18 +54,18 @@ when calculating the displacements of the 4 masses? Include the analysis and res

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

6. Use `chol_tridiag.m` and `solve_tridiag.m` to solve for the displacements of hanging
**6\.** 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.

![Spring-mass system for analysis](./figures/spring_mass.png)

7. In the system shown above, determine the three differential equations for the position
**7\.** 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.

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


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